Evil Species

Demon are spawn of higher demon and are feeding by the soul

Soul Swallower
More known as "Deadites" or "Army of Darkness" (because this name is never canonical said) they are the spawn of the Evil Force, they are the main antagonist of the "Evil Dead" saga. They have much power like levitation or the possession of anything like tree, dead, animals or even Reanimated.

Semi deadite
This subspecies is the species of the ex deadite. We know only three persons Ash, Sheila and Mia (from "Evil Dead 2013")

Spawn of Great old ones
They are the rake-like demon from the tv Show "Ash Vs Evil Dead". The only differences with deadites it's that they have totally black eyes (instead of White or red in somes comics) and their demonic form is similar to the Crawler from "the descent".

Soul Sucker
This species is a subspecies of the deadite (according to "Army of Darkness vs Bubba Ho-tep"), they appear in "Bubba Ho-Tep" and the crossover with Evil Dead. They have their own Necronomicon, the Necronomicon Ho-Tep, contrary to the deadites, they (apparently) cannot possess somebody else (even if the crossover is a little bit confusing with their skills). Like the Kappa in Japanese folklore, they swallow soul by the ass.

Spawn of soul Sucker
These spawns are gigantic scarab who obeys the Soul Sucker, and the Soul Swallower.

Slasher
"It's a type of undead, I guess... Sort've like a vampire or a zombie, they're so full of anger that they don't wanna die. They hate love, youth, sex... Things they miss from life. The Holy things I know for sure is that they're mean and hard to kill".

They are the mains antagonists of Hack/Slash comics,in "Slice Hard" we learn that they essentially emerge during the 80's. They appear in almost every license: they are inspired by Jason Voorhees since "Jason Lives" and explain how he's still alive in "Part 2", Chucky's mentioned to be one of the most known slasher ("Hack/Sash Vs Chucky") they are sub species of deadite, even Herbert West work on them in his past (by the way, if we inject the ReAgent to a dead slasher he briefly became human). In german they are named "das Haumesser"2

Repeater
This is the species of Victor Crowley (named in "Hatchet II") they are slasher but more imaterial.

Dream Slasher (spawn of Dream Demon)
This subspecies is first mentioned in "Hack/Slash land of the lost toys". They are totally based on Freddy Krueger, even if in the comic they never mentioned Dream Demon.

Soul Tearer (Cenobite)
This name is never canonically said, it's a reference to the worldwide tagline of "Hellraiser". They are spawn of the Leviathan. Evil Ash says in "Tales of Army of Darkness" "I'll tear your soul apart". This demonic specie defend the order and are spawn of the Leviathan

Pseudo Cenobite
This branch is cenobite not made by Leviathan, either human in "Hellbound" or Cenobite in "Hellraiser III" or "Hellraiser 4".

Cenobite pet
This is the pet higher cenobite

Eremite
They are kind of spawn of cenobite, they serve them in abducting human in Leviathan realm. They all lookalikes as homeless and they transform themselves in kind of skeletal dragon.

In "king for a day" we can see briefly dragons, they could be a non conic representation of them (in this comics Deadites have red eyes). We can also see some that look likes them in "Revenge of Hitler".

Deader
This is subcategory of undead, they are made by cenobite magic. They appears in a the comics "Clive Barker's Hellraiser 17" then in the movie "Deader", we don't know if they are really link.

Hell Brigade
They don't have canonic name. The damned are humans not transform in Cenobite when they open the box. They are essentially skinless even if they can steal the skin (and the strength) of the men they killed. In "Ash and The Army of Darkness" a deadite (the Faceless man) transform the knights that he kills in skinner.

Abaddon's troop
This is the equivalent of cenobite from the army of Abbadon. They only appears in "Dark Watch".

Cherubim
This the Hellraiser counterpart of the christian cherubim, they are based on Abbadon's grasshopper in holy text. they only appear in "Dark Watch",we learn that during the revolution of Satan they decide joined God.

Archangel
They are the most powerful category of Angel, they only appear in "Hellraiser Judgement". We only know Jophiel.

Angel
They are classic angel, they appear in "Army of darkness Vs Army Of Light" and "Army of Darkness Vs Marvel Zombie".

Fallen Angel
They don't really have name, they are possessed Angel, they appear in "Army of darkness Vs Army Of Light" .

Bloodsucker
They are basically vampire as seen in "Army of Darkness Vs Classic monster" or "Furious Road", they can turns themselves into bat,are vulnerable to wood, sun and cross (not only christian cross), sometine they are pale sometime not due to retcon.

Bride
They are Praetorian vampire protecting Dracula (as seen in every adaptation)

Dhampire
Hybrid between human and vampire, they can live in the sunlight. The only one we know is Eva the Daughter of Dracula.

Cosmic Bloodsucker
They are green extra-dimensional-shapeshifter being, they can take any form and can fusions to become a Kaijuish aabomination. They work like xenomorph, mind hive, and serve their masters, named Big Mama (who are basically a giant Cosmic bloodsucker) by giving hit human body (Bubba Ho-Tep vs Cosmic Bloodsucker).

Source
1"Hack/Slash Euthanized"

2"Hack/Slash #12 2011"