Okay, so speculating on projected details for Valinor's invasion, it involves local forces stripping their defenses plus the incoming crusade fleet, At a local force of 32 billion guardsmen plus the transports, troops, space marines and superheavies brought by the crusade fleet it is safe to say that the crusade will be more limited by transport capacity than troop availability, and their fleet will be hundreds of capital ships and tens of thousands of escorts strong.
Assuming the presence of elements from multiple corrupted Space Marine Chapters and billions of Golden Legionaries is safe, the question is in whether space marine elements will exceed two thousand in number and whether the Abomination aligned Mechanicus will send a major contingent, thus allowing them to field Titans and such.
Keeping in mind that a crusade fleet is a full campaign they might either decide to focus entirely on wherever Saint Lin is(I suggest either Avernus or Svartalfheim based on defensibility, considering Svartalfheim is a different religion I suggest Avernus), or launch diversionary attacks throughout the Trust and a main strike towards Lin, or launch a set of serious attacks towards targets of Importance(Lin, Midgard, Vanaheim), or strike a lightly defended point we will move to defend(a colony) then take advantage of their faster Daemon driven FTL to launch deeper attacks towards their real targets.
Culturally tradition and obedience are their best advantages and worst problems, their military tradition means they fight competently but means that they fight predictably and we have copies of most of their training manuals, while their focus on obedience makes them unbreakable but will impair efforts to act with their forces split, despite a high probability of the crusade fleet at least retaining Astropathic comms, and prevent them from pulling out before they take too much damage.
Considering this I expect them to either strike directly towards Avernus or take a colony then strike towards Avernus when we move in response. Likely following Imperial guidelines towards subduing enemy human groups by taking out key figures and resources in a gratuitous display of excessive destruction aimed at demoralizing the rest of their enemies.
If we're lucky the corrupted Space Marines attached to the Crusade will try to Exterminatus Avernus.
I doubt we'll be that lucky.
Assuming they don't take us out through massed bombardment(they won't, Avernus might react beyond the norm if Chaos is bombarding the surface, Imperial tradition is to avoid risking the ships, Duat has a Sun Beetle population, this is 40(+)k, they have way more Infantry to spend than ships)
then when they land they have a significant disadvantage compared to Garkill's Orkz, they can't drop organized forces directly on top of us, or really anywhere near us, considering their lander design and our heavy AA, and they can't easily teleport troops to their landed ships.
Considering most Imperial crusade's lack of emphasis on air-power and the anemic air wing support on escorts, I'd suggest getting some Vanaheim air-forces transferred over in advance then launching a massed airstrike on their landers, or maybe employ psyker choirs against them, or use the Phase Tigers and stealth psykers to plant charges and missiles to take out their landers, they'll likely have at least a partial counter but with the sheer size of their forces any damage to their landers will slow down the rate they can land forces, leaving them exposed to wildlife longer.
They'll then have to march overland, under Macrocannon bombardment at a certain proximity, as Chaos aligned beings, on Avernus, they'll get shredded.
At which point they will face whatever Trust Forces and local elites we can Precog/Schrodinger's army into position to face them.
I assume their forces will mostly be equipped in line with the Imperium's favored logistics, IE. as cheaply as possible because they want to lighten the supplies burden. But will the infantry have mostly Impalers or Lasguns? it's an important question because I'd expect troops in power armor to take on around twenty times their number of lasgun guardsmen, especially inside familiar cities on the defense, but only around two to five times their number of Impaler guardsmen.
Our city walls and artillery positions are impressive but It's really the house bunkers and prefabricated fortresses that will reduce the effectiveness of their siege artillery the most.
Their biggest threat is likely to come from the way the invasion will outnumber the entire population of Avernus combined, absent serious Trust reinforcements.
The biggest uncertainty is how they will use their space marines, will they use them as to create breaches for a breakthrough, or will they strike at critical points? and when? What other elites will they have?
And how will they use their Psykers/sorcerers? Probably Angyl summoning rituals, some potential to split them up among their forces as support but it's less likely.