So, about Chaos, and the behavior of it's members.
SANITY IS FOR THE WEAK
Except not really. Chaos is full of crazies, of course, that is true what with the gibbering of demons, the negative effects of direct warp exposure, a lot of the things the Chaos Gods see fit to 'gift', and the simple fact that a lot of people join Chaos because of finding themselves in terrible, often enough mindbreaking circumstances and turning out of desperation, in conditions that have broken them and killed many around them.
Nevertheless, the behavior of individual chaotic groups is shaped by not only their personal circumstances and knowledge, but also the constants of what the Chaos Gods want. With a nameless cult or warband who have essentially stumbled into Chaos, their understanding will be crude, vague guesses based on limited information, with a lot of the procedures they have being 'workable but ultimately wrong' guesses combined with a hefty dose of 'don't even think about going near that' for the things where members of the group exploded for doing it.
So, for example, a Khornate force might be under the impression that Khorne hates shooting people, but that's not really true. He doesn't particularly favor it, but, you know, Khorne Berserkers carry pistols for a reason. No, what Khorne hates is cowardly standing back and killing from safety, and also killing without bloodshed. The former, of course, describes most usage of heavy weaponry, artillery, and simple taking cover and firing from the safety of behind a wall or whatever. The latter describes, for example, killing people with Flamers. So, while Khorne has no specific objection to guns per se, when all of the members of your Khorne invoking cult who stand back and shoot people find themselves getting punished, it's fairly easy to draw the wrong conclusion and just stop using guns, because you don't want to share their (terrible) fate.
Whereas for 'workable but ultimately wrong', you might see a lot of people who, for example, interpret Tzeentch's love of plots as a love of caution, which he doesn't hate, and if your idea of MAXIMIZE CAUTION is contingency after contingency after back-up plan after secret strategy after... well, then you are hitting his 'plotting', his mild complexity addition, and honestly probably his love of ambition. So you might have a workable rubric for keeping Tzeentch reasonably happy without really being right or even particularly close.
Older, more experienced groups will tend to have a more accurate, more complete understanding, but they can still be wrong. They'll be less severely wrong in a functionality sense if they are wrong about something, but in terms of the why's they actually can be just as badly wrong.
Now, when I say that the behavior of groups is shaped by what the Chaos Gods want, I am not just talking about a fear of punishment. I'm also talking about the simple fact of rewards.
So, for example, a Khorne Berserker is stupid or crazy for charging a tank intending to chop it in half, right? Only, well, by solving all his problems with AXE TO THE FACE, he's been getting rewarded by Khorne. Since he does it so routinely, perhaps he can charge down a Baneblade, shrug off it's iconic eleven barrels of hell, and chop it in half with his axe. And hey, maybe when he started, it was a primitive, tribal, stone axe, but having pleased Khorne so consistently for so long, he now has an axe with a Bloodthirster inside, a powerful demon weapon that breaks reality and reason alike. Oh, and doing it again, charging down that Baneblade, cutting down the crew and chopping up the infantry behind it? He gets another boon, one that makes all his future fights easier, and justifies taking a tactically unsound approach to gain long term benefits, like some kind of demented RPG character.
So, how do the big legions fight and why is that smart?
Let's go over them one at a time.
The Black Legion
The Black Legion is more of a military unit of Chaos than a cult of such. Accordingly, the Black Legion mostly fights in an expedient way, implementing unique tools like Daemons but not focusing on the pleasing of the Dark Gods over actual mission success. There's not much to say about them, as a result, since anything they are doing to please the Ruinous Powers aside from 'winning' is not particularly affecting their strategy visisbly.
The World Eaters
Blood for the blood god and all that. The World Eaters engage in bloody close combat, disdaining many safe practices like 'bombardment' and 'stealth' in favor of maximum bloody carnage, which of course gets them the blessing of Khorne and means they can get away with being 'stupid', because, you know, that Khorne Berserker doesn't really need to hide when your anti-tank rounds are plinking off his chest, and he doesn't really need supporting weapons when he can chop up anything in his path, because, again, Khorne. Direct assault over clever or careful tactics everytime, which, you know, if they were imperials would be moronic, but since Khorne rewards them for it... They're scary and have a lot of reason to not 'fight smarter'.
The Emperor's Children
A quick check of Lexicanum tells me the Emperor's Children frequently use impractical armor, raid for slaves, and, of course, have a lot of Noise Marines. Since Noise Marines are indulging in an excess of sensation as a part of their combat doctrine, not to mention spreading around said sensation, since, you know, their enemies aren't deaf (before they shoot them, at least). All in all, it's fairly easy to see how most of this behavior might earn them Slaaneshi gifts, and when going down the impractical route makes you so much better than you would be otherwise, it becomes increasingly easy to get away with 'bad tactics' as the divine gifts pile up.
The Death Guard
These guys have some very blunt aspects- spreading disease and ruining worlds in the name of Nurgle- and some less blunt aspects. For the somewhat less obvious, we have their preference for steady, inevitable advances- a tactic that invokes Nurgle in the form of inevitability and despair, as the opposition has plenty of time to see they are doomed before they die. In a general sense, Nurgle will typically reward slow but sure tactics over quick, decisive ones, and of course the central Nurglite advantage is absurd levels of durability- which supports marching straight at your foe in the open while they shoot you, making that easier to do.
The Thousand Sons
They covet knowledge and magic and have significant psychic abilities. They sow change, gather knowledge, most of them are highly ambitious... They fit Tzeentch to a T in short, even before the whole 'arranged to exist as they do by Tzeentch' detail, which might bestow some degree of natural functional favor. Of course, the Thousand Sons are in a bit of a strange place, given that an awful lot of their fortune, good and bad, seems to be practically a maniacal in-joke by Tzeentch, arranging for them to do a thing and succeed spectacularly or fail terribly.
....
You know what, I'm a bit wrung out right now, I'll get to the others tomorrow hopefully.