You're Doing Undead Wrong

Undead are more than acceptable targets for any kind of adventurer. We should not let this terrifying force of un-nature be just a different flavoured sack of HP that maybe is susceptible to holy water. It’s totally unfair towards the pure distillate of terror those monsters can be, if only you let them be as scary and invincible as they deserve!

Yummy.
Zombie from Resident Evil 2 Remake.

Ok, maybe I played too much Resident Evil 2. But that rant is not that far from the truth. I think that, rather than just have a weakness to holy damage or fire damage or the such, each kind of creature should fundamentally be unique, and understanding them to defeat them or work around them is a challenge all on its own and worth exploring. And once the threat is understood, seeing players interact with it in different kind of ways and seeing them find solutions to outsmart, avoid or use it makes for an hell of an interesting game. That’s an extremely valuable lesson I took from comparing RE2 to other zombie games. Did I already say I liked RE2?
Anyway, that’s how I plan to revamp undead at my table. I don’t plan to use all those rules at once, except when I will because I want players to hate me. Mix and match always makes for a good time.

Arise, my warrios!
Settra the Unperishable from Warhammer Fantasy.

The Restless
Some undead don’t die. That’s a fact. Whatever inhabits that weapon of putrescent flesh that’s shambling towards you can’t be just shanked out of this world. They are not like you.
After being defeated, Restless Undead come back up after d4*10 minutes to try and eat you again. They are the reason corpses keep disappearing from the dungeon.
Each Character can spend 10 minutes keeping them down, sitting on their shambling remains and hitting whatever tries to rise again. Up to 3 Restless per Character can be kept down, preventing them from coming back.
Each Character can spend d4*10 minutes to utterly dismember a single undead, destroying it for good. Alternatively, it can always take 10 minutes if you use something appropriate, like oil to burn it down, nails to crucify it somewhere, or a chainsaw to make sure it is appropriately scattered all around the room.

"I live... again!"
Tchernobog model used in Blood development by Monolith.

The Recreated
Some undead did die. And somebody around them was not happy with that turn of events. The scuttling claws and broken bones, gathered by madmen, found unlife anew. Hulking horrors stitched together and grafted to each other, in a perennial state of walking destruction, held in one piece by thin wires and threads of hate.
Recreated Undead have 3d4 limbs attached to their grotesque bodies. Half of them can be used to attack everything in range with a single Action. They gather 1d4 more each time they kill something and spend 10 minutes tearing the corpse apart. They can only do so with the corpses they kill themselves.
Instead of dying, they make a Save. On a successful Save, they lose 1d4 limbs. On a failed Save, their flimsily put together bodies fall apart like they were always meant to.

I've waited waaaaay too long to find an excuse to use this one.
The Curse from Dorohedoro by Q Hayashida. GO READ DOROHEDORO PLEASE.

The Revengeful
Some undead are simply dead. They linger on, and the violence that unmade their lives lingers on too. Ghosts of murders past and future, stealers of killing intent.
The Revengeful are incorporeal. They won’t attack unless they sense a killing intent, regardless of who it is directed to, in their area of action. This area extends 10 feet around them, and a faint glowing mist hoovers in it, like a stagelight.
When they sense the intent, they start audibly screaming. The mist becomes blood red. Your hands are actually covered in blood. You are actually covered in blood. The screams come from you now. They start haunting and attacking all those involved in the current conflict, inflicting constant damage as they ravage their victims with spectral teeth, claws and broken bones. They follow everyone involved until something drops dead. Those killed strengthen the Revengeful and sate its bloodlust for a day, giving it peace for a few hours.
They are spitefully condemned by themselves to relieve the key moments in their violent end. During this theatrical dance of death, they disappear every d4 rounds of reenacted suffering and silent screams, to reappear in the next spot of this macabre play. There are usually no more than 3 key spots/moments, that are forced to relive in loops for all eternity.
This ghastly, continuous rehash of their violent deaths can and should give out some important features and information on the dungeon, of course.

That's gonna take some time to clean up.
Screenshot from DAYZ.

HP, Speed and whatever else
Just make them fuckin’ slow and avoidable. One thing that the latest incarnation of RE2 taught me is that the undead are a fuckin’ phenomenal trap, and a not so great straight up fight. Fighting them is unreliable. Or at least, make most of them so. Exceptions are always a good time.
I make them move 10 feet per turn, inflict a good amount of damage (3 Afflictions, which is roughly a d6/d8 in B/X terms, probably not outright lethal but very scary) with a pretty high bonus (they reliably anything that’s not armored), and they go down as soon as they receive an Injury ignoring Afflictions (so they would have, like 1-2HD, but ignore all the damage that’s less than 4).
Being so slow and damaging, they are dangerous in numbers or in close quarters with little space of maneuver, which is pretty much how I think undead should work as interesting elements in a dungeon anyway.
I think I’ll have fun running them. I can’t really tell for my players, however I hope their screams and improvised plans to salvage the situation will be entertaining.