I guess this should be at the top now that the Min-Max Battalion has marched over the hill: yes, I am aware this is silly. Yes, I am aware you can use [Helios] to hold Gladiator mods, I pretend that isn't a thing because I switch pets around quite a lot. Yes, I know a status build produces larger numbers, yes, I have actually used a Status/Condition Overload build in-game, the only real difference that was apparent to me, I stress that was apparent to me is that enemies die a little faster in Steel Path before the conditionals are all up and running, which sometimes does not happen because this is a crap Status weapon. (<--- boy a lot of THAT doesn't matter after the Great Melee Nerf of June 2021, lol guess who didn't need to worry about it at all) In point of fact, this is a crap weapon, and if I cared that much I wouldn't be using it to begin with. The point of the build is "Use cool-looking weapon and make it cause pretty red numbers to pop out of enemies," and the guide is long because it happens to work okay.

The Basics:
Working any of the Warframe-equippable Gladiator mods (Finesse, Aegis, Resolve) onto your frame will further increase crit chance, but it's not that important, you'll red-crit eventually anyway and there are other ways of adding crit chance to begin with, like Wrathful Advance or a riven.

Post-36, the build basically works the same because we're in the same situation where we have damage types that do at least normal damage to make up for damage types that do less, so even though pairing Impact and Corrosive is now more effective against Grineer, everything is still covered well enough that it will die when the crit is stacked. This is most obvious with the Infested where low Slash means we're not hitting them very hard, but they still don't have enough HP to survive normal damage with crit stacked up.

(The smart thing is probably to swap Corrosive out for Magnetic to cover Grineer and Corpus with buffed damage, still relying on the Infested having low HP and also gaining the benefit of extra damage against overguard, I just haven't bothered yet.)

Also Wrathful Advance exists now and brings with it a different brand of crit insanity..

[Helios]
If you're using [Helios] for Gladiator mods, drop them from War, replace them with Weeping Wounds and Condition Overload, replace the elementals with the 60/60s. If you want to be silly you can replace one of those with [Saxum Thorax] for additional status and impact damage for enemy shields, but swapping either [Weeping Wounds] or [Condition Overload] for that probably won't work as well even against those shields.
Gladiator mods attached to [Helios]' weapon no longer apply to the player's melee weapon, so the options for dropping the Gladiator mods are "get a riven with crit chance," "use [Kullervo]," or "use Helminth to put [Kullervo]'s 'Wrathful Advance' on another frame."

Rivens
Crit Chance is the obvious important stat. If you can pull or reroll a Riven with +crit chance, it will push War's crit above 100 before Blood Rush/Gladiator buffs. For those of you who can't live without status, it also lets you swap to a full status build more easily, and there are other Riven buffs after Crit Chance that can be useful. See here for details. With the nerf to [Condition Overload], the full status build isn't nearly as better as it was, however, (although it's still an extra 20k or so per hit) and it's probably not worth investing in a riven if you're not willing to reroll it to get two other good stats to go along with it. Since no one likes [War] because it isn't meta, you can probably get a riven for cheap, especially if you're sitting on enough kuva to get a crap riven and reroll it.

Focus
Nothing really required, but Naramon is the obvious choice for the melee bonuses, including making it easier to keep a combo (which, like crit chance itself, now has other alternatives like [Rauta] and the dexterity arcanes.)
Madurai is a valid choice just for buffed damage. There's Void Strike, and the passive buffs to physical damage.

Specific Situations

• For dealing with your Lich/Sister, just switch for its weakness. Heavy Blades have long enough range that you can [Swipe] at the Lich from farther away than it can grab you, just be careful to only use the first attack of your combos so you don't accidentally get closer. The first hit of the "hold forward while pressing the melee key" combo for Tempo Royale is excellent for this. If your frame is built tanky, or you're just using Rhino/[Rhino Prime] or something else with high survivability you can YOLO it and just spam your combos, as Iron Skin should save you from the lich's grab; I want to say spamming and losing the time on target during the grab animation is more efficient than poking it from further away, but I don't know for sure.