I must preface this by saying that I know basically nothing about WH40K lore, so my opinion on this class is purely about balance.

Base Chassis

HD, skill list, weapon proficiencies, saves...all comparable to the Barbarian, so that's cool.

Green Skin

Hrm...definitely makes the class less MAD, but that's one of the things that helps balance the Barbarian's AC (that they can't just tie everything to Str and Con, dumping Dex). Something to keep in mind.

WAAAAGH!!!

Seems appropriately thematic, but I'm not sure about balance. At the low end, it seems like a reasonable trade-off, but at the higher levels, getting tons of extra damage to dump your AC into the sea is...questionable. Beyond how a the general advice of RPGs for awhile has been "a killer offense is the best defense" (aka "the best way to make sure the enemy doesn't kill you is to kill them first"), 5e isn't balanced around this kind of thing: my understanding of how bounded accuracy applies to combat is that a characters ability to take down a creature isn't measured by their ability to hit the creature (which should be solid even against powerful foes), but rather is measured by their ability to deal enough damage to take out a non-neglible number of another creature's HP; similarly, defensive capabilities are not primarily measured by being impossible to hit, but by how much punishment you can take. Giving up points of AC (a secondary defensive aspect by designer intention) to increase damage (a primary offensive aspect by designer intention) feels...off. I'm not sure if this is a huge balance problem, but it's the best I can think of to articulate why it comes across as potentially problematic, especially at the higher levels. If nothing else, past a certain level, you're either going to only do a small dump, or you're going to do a full dump; if you're an Ork 20, and you're facing something that can hit you no matter what, there's no reason to only dump 10 points of AC when you can dump 20. Oh yeah, and it also further reduces your need for Dex; that you get features that replace Dex for to-hit and AC boosting at level 1 seems iffy.

Beyond the potential balance issue, how long does the trade-off last? One attack, one round, until you use the ability again to change the trade-off level?

Color

These both seem fine, balance-wise; that said, the stacking +1s to Stealth don't really fit with the idea 5e has of avoiding stacking a bunch of numerical bonuses...but the game doesn't exactly do that everywhere, especially when it comes to Stealth.

Fighting Style

Seems appropriate enough, and balanced enough.

Extra Attack

Seems appropriate/balanced enough.

Improved Critical

This seems fine; little iffy on giving this to anybody other than the Champion, but I guess it's not a huge issue, especially since it comes on so much later. Plus, at least Champion upgrades it at level 15...

WAAAGH!!! Improvement

Super-weapons only you can wield? Not sure how to feel about this, personally, but I guess Paladin gets both a constant extra die and smiting, so it's not too much more than that.

Improveder Critical

...and yet Ork gets the improvement earlier than Champion does? I mean, okay, I'm not even entirely against them getting it, but at level 13? This should probably be delayed to 15 or 17, IMO.

Da Biggest And Da Best

Comparable to the Barbarian capstone; you give up +2 to Con/Con max, in exchange for a constant Enlarge effect (advantage on Str checks, +1d4 weapon damage, AFAICT). Seems balanced enough...well, on its own. Pairing it with other things (Green Skin, for example) is potentially OP, but that's only if Green Skin itself is OP.

Painboy

"Dok" seems appropriate without being too powerful.

"DokTor" seems like a good upgrade, and the anti-pain option is amusing. I think "advantage on Con saves" is significant enough that the number of skills with disadvantage should be more extensive; my gut says "all Int/Wis/Cha checks, but not saves", but that seems like it might be going a bit too far.

"Mad Dok" gives an assigned expertise, which keeps it from being a bit questionable, and the healing rate is slow enough and limited enough that it too is balanced.

"Sane(?) Doc" seems fun, although a couple more effects would be appreciated. Also, while it seems heavily implied to me, I could definitely see somebody arguing that you should be able to give yourself Fury to stack with your WAAAGH!!!, which I feel plays into that "may as well keep dumping AC" problem that WAAAGH!!! already has at the high levels, so specifying that you can't use "Sane(?) Doc" on yourself would be helpful.

"Medic" is fine as far as the increase in healing magic goes. But triple proficiency for Medicine? If it were any other skill, I'd put my foot down; that it's Medicine just means that I'm only extremely uncomfortable with it. And making your "Mad Dok" regen 1 HP/round seems slow enough that it's still not a huge issue, although I should make sure to ask if this also upgrades the "Sane(?) Doc" ability that grants your "Mad Dok" regen to a party member.

Can't judge the other sub-types yet. Overall, a couple definitely questionable things, but I don't think taking Painboy from 1 to 20 in a real game would prove too problematic; sure, it doesn't get a ton of healing magic, but at the same time, it would be similar to a Barbarian with a healing twist.