Force projection in the 42 millennia
In the 42 millennia, the different factions' ability to have their influence felt across the galaxy dictates some of the tactics they use and some of their interactions with each other.
The Brutal steamroller
These ones are the ones that once they get a head of steam, they carve huge swaths of destruction across the galaxy in pursuit of their goals. Their historic ability to pull this off means that most other factions' interactions with them are dedicated to preventing them from getting to the point that they can build this momentum. It also leads to most of their activities being targeted towards reaching that tip over point.
Moreover, another thread of these brutal steamrollers is that they are widespread enough that they can always build up that momentum in isolation and manifest as that steamroller which means the other factions have too actively hunt them down.
Into this category we find Chaos, Orks and Tyranids
Chaos
Chaos is a corruptive presence in the galaxy, and once it fully takes hold of a world, it's almost impossible to take that planet back. Its main issue is that the bulk of its forces need a lot of set-up to manifest and sustain themselves.
The fact that it doesn't need a dedicated force to spread itself, only to ensure that its growth is uninterrupted, means that it doesn't value any particular unit in its forces so no loss permanently affects it, but getting to the point that it becomes a galactic threat from any single world is a long shot.
The biggest threat is as a weathering force because it ensures that no infrastructure is ever secure, and that the other factions can't safety build up forces.
On the other hand, it also means that any minor incursion has a good chance of auto cannibalising itself if left alone because there is no structure providing guidance and every member of the incursion is out to come out on top by betraying their colleagues.
But when it does build that momentum, its corruptive presence means that the wound it cuts across the galaxy keeps bleeding for centuries afterwards.
This means that it can afford to just throw weak forces at the opposition while they build up at no real cost to themselves because the other factions must respond else, they face a major threat.
It also reflects the mindset of the chaos faction were sacrificing 99% of your guys to gain a chance at ascension is standard behaviour.
Orks
Orks can be likened to a viral infection across the galaxy that's at a late stage. They are already far to spread out to make any form of containment by the other factions viable, and their no real way of getting rid of them once they've set up on a planet that leaves the planet habitable.
The only option the other factions have is to treat the symptoms by regularly culling the Ork population.
The issue there is like a virus, if you fail to treat the symptoms the Orks grow in population and jump up the Tech tree to the point that they both outnumber, outgun and out tech you.
They're a threat that isn't subtle, but requires a constant resource drain to contain, because if you don't it will build up momentum and topple you.
The biggest threat is as incurable problem because it forces you to dedicate some resources to combating a problem were if you ever undersubscribe the response, you'll need to dedicate even more resources to get back to where you were.
Once it builds momentum, it is the most powerful faction in the galaxy, and barring the entire hive fleet showing up at the same time, and the necrons experiencing a mass awakening, it's the only faction that has its win condition within reach.
This means that the faction can continue to do whatever it wants and have fun, because they're ahead enough in the game that they might just stumble over their win condition.
Tyranids
The tyranids are best compared to a boulder rolling down a hill. Their nature means that after noming 1 or 2 worlds they have a fleet capable of taking far more. It's to the point that you can never be sure you've taken out a hive fleet because if a single ship makes it to a world incapable of stopping it, then you'll be seeing the same thing again at full strength a few years down the line adapted to the techniques you used to put it down last time.
The only option other factions have is to kill on site and actively search to ensure you've gotten every one of them.
The biggest threat it poses comes in the form of genestealers, as they can ensure that the hive fleet never truly dies by setting up fights that it can win and gain biomass, and ensuring that the battered remains of defeated fleets survive long enough to get back to full strength.
They've got the most efficient steamroller build and its shows in that every other faction considers them an apocalypse whenever they show up for reasons beyond ideology and will actively work together to stop them.
This means it can continue to use the same overall strategy because it only ever gets stopped by increasingly desperate strategies that won't work a second time, so providing it has enough fleets incoming, it's almost guaranteed a win long-term.
The IoM
The IoM also technically occupies this category as when it can bring its full might to bare, it wins conflicts in the 42K. The issue is that it's involved in so many concurrent conflicts that this almost never happens.
The other factions know this so they engage the IoM under time pressure to either achieve their goals before the IoM can respond or fortify enough that the cost benefit for the IoM no longer makes taking it back worth it.
They're an omnipresent and known threat that can be managed, so other factions have well thought out strategies for achieving their goals, that only ever fail due to:
· The IoM getting its act together faster than expected
· The IoM performing far better than expected.
· By some miracle the PDF speedbump impeding them for longer than expected
· Their own time pressures making it so they can't get the resources required to guarantee a win.
The fact that they're a known factor in most faction plans, and that they don't have spare resources means that they are mostly a reactive force, and mostly concentrate on either holding what they have, or building up resources to react to more stuff.
The house in a Yellow Nuclear Submarine
On the other end of the scale you've got the forces that rather than building momentum and hitting like a hammer, perform more like Indiana Jones and just pull out a gun and shot people rather than getting involved in protracted conflicts to achieve they're goals.
They tend to have the man to man highest quality troops and tech, but very small numbers, and massive entitlement complexes from the war in heaven
Moreover, they are spread out enough that in theory the larger factions could crush them if they concentrated their forces but hold such disproportionate power that they could wipe out any force that tried this.
Into this we have the Eldar and the Necrons.
Eldar
The craftworld Eldar are a technically dying race. Due to Slannesh, their birth rates are down, but in theory, if they could avoid conflict, there's no reason that they couldn't sustain a steady population growth.
The issue is that they don't want to just live on, they want to get back on top of the galactic pecking order and pursue what they believe to be their duties in keeping the galaxy in order by stopping Chaos and the Necrons.
To do this they employ Farseers to grant them intel and visions of the future so that they can guide the galaxy to one more of their liking.
There's a joke about 6 eldar vs a 6-man space marine squad. It goes that the squad would kill 5 of the eldar with ease, and the last one would do the same to them because whatever form of combat it was, they would be the best person there.
The eldar have the best special forces in the galaxy (enforced monofocus for centuries in whatever profession you're doing will get you that) and between that, some of the best tech in the galaxy and farseers manipulating people and the future, they can influence conflicts across the galaxy to go in the paths they prefer.
They wield power far in excess of what military they have, but most importantly, they're protected from major reprisal by the same specialised force.
The Eldar have the forces to destroy any imperial target they choose. They have the knowledge of where the vital organs of the IoM are. Any major conflict between the IoM and the Eldar would end in the Eldar near extinction and the IoM dead as an organisation.
Both sides know this, so the IoM is forced to just take it when the Eldar do things to them and exercise serious restrain in any reprisal.
The Eldar employ the minimum Eldar force they think is required to get the job done and fill up the rest with unknowing allies. They project forces far and wide because they still want to control the galaxy and employ what little they have to maximum effect.
Necrons
The Necrons might be the smallest major faction population wise. If you just consider the active Necrons, there might be less Necrons in total than either tau or craftworld eldar.
They are also the only faction to still have use of all there best gear, and that gear was potentially the most potent in the history of the galaxy considering they we're winning the war in heaven against the combined might of the Krorks, the Eldar backed by the full pantheon and whatever else the old ones could cook up.
There used to be a meme about the Necrons. "Our most basic gun can wreck your most advanced Tank. In one shot. This is fair and legal."
What the eldar achieve through careful planning and heavily specialised troops, the Necrons do through being that much more advanced than everyone else. They don't project military force and influence galactic affairs as much as wake up and tell people to get of their lawn. The scary thing is that they're strong enough that this not only works but has netted them quite a bit of territory with other factions requiring extreme numbers advantages to be competitive.
In terms of galactic presence, they're an elite force that's taking whatever territory it feels like because they held it millions of years ago and don't feel being absent since dinosaurs walked the earth would mean anything to diminish the claim.
The only reason they fall into the same category as the eldar in terms of force projection is that due to the small number of them active now, the effects of there actions are similar in terms of forcing factions to behave as dictated by a smaller more advanced force, and handing it work most of the time.
Piggy with a Stone house
The last category would be for the factions that operate from a single stronghold, that would cease to exist of it ever fell. Like ant to an anthill their behaviour and actions are restricted to the area immediately around their bastion
They act to bring resources back to their bastion to help fortify it and ensure the prosperity of those who live there and given the opportunity act to increase the size of this stronghold.
Their forces tend to be geared entirely around this resource gathering activity with the homebound forces dedicated to supporting it.
The Dark eldar and Tau fall into this category.
Dark Eldar
After the Fall of the Eldar, the ones who decided to double down on the behaviour that got them into the mess in the first place became the dark eldar.
Based out of Comeragh, a set of Webway dimensions bend into the shape of a city large enough to have 2 suns installed to provide light, the dark eldar might be the largest faction of post fall eldar If only because they have both functional immortality and can sustain a growth population.
They require a constant stream of suffering to sustain themselves so are restricted from taking long forays out of the city, which can provide the highest grade to keep them hale and hearty.
Unfortunately for the rest of the Galaxy, they are also the Eldar faction to retain most of their WiH and prefill tech. This means that 'near Comeragh' is essentially every planet in the galaxy. To make things worse the resource they take back to sustain the hive are sentient beings whose fate is to suffer unendingly to sustain the masters of the Dark C. There is a reason they gained the tagline "Pray they don't take you alive"
In terms of force projection, they're malevolent vultures that will only take the most vulnerable parts of a faction, raiding nests while the armies are away, or entering a battlefield when all parties are exhausted.
They have harassed every other faction in the setting, and no-one would stop you if you tried to kill them.
They escape reprisal by virtue of there stronghold.
Comeragh is virtually impossible to access by anyone but the Eldar. Moreover, even if you could get inside, the stockpiles of WiH grade weaponry, the borderline impossible to navigate geology/geometry and shear number of Dark eldar means that any faction that got that far would get torn to pieces.
If the entirety of the IoM tried to invade, there's a good chance they'd fail. In fact, the only successful incursions into the Dark City were either plots by a Dark Eldar to kill another Dark Eldar, or manifestations of an Eldar God.
The Tau
To the exact opposite of the Dark Eldar we have the Tau. The only race that's still trying to be Good at the Faction level rather than seeking pure survival.
Based out of Tau space, the close proximity of Tau worlds allows them to remain an empire even when they lack true FTL comms and must rely on the interstellar pony express for comms.
This makes Tau space a stronghold as all the worlds are close enough by default to be able to rapidly reinforce themselves. Moreover, the lack of the option to just travel to a better world means that any Tau world tends to be much more heavily developed than a random world recently captured by the other factions.
The tau military, spacefaring, diplomatic and engineer castes are all dedicated to capturing more resources to improve the stronghold like how the dark eldar. But the resources the Tau gather are other races and worlds, partially to help fortify Tau space and provide strategic depth, and partially because their philosophy dictates, they induct all they can into the greater good.
As such, in terms of force projection, they are benevolent vultures, taking worlds in close proximity that they believe would benefit from the greater good. The Tau identify target world at the borders of Tau space, and by hook and by crook integrate it into Tau space. Then they repeat the process.
They escape reprisal for this via the strength of their stronghold exceeding the amount of effort the IoM is willing to expend retaking the worlds particularly because a Tau captured world only has a manpower cost associated with recapture and reintegration in comparison to the amount of additional effort required to get one back and functional of the Orks, chaos, tyranids, necrons etc.