I had an idea for a character. I get the attronach bithsign, and use absorb magicka weapons to refill my magicka. RPing that I am unable to generate magicka of my own, but rather steal it from enemies. But I have a question, which enemies have magicka that I can steal? It's safe to say that anything that can cast spells have some, but what about non-spellcasting enemies like skeletons, zombies, bandits and marauders.

Interesting idea, just had to look in the construction set. Looks like it's up and down beers have 5, ogres has 0, spellcasters has more: Imp: 60 Spriggan: 51, however boss level spellcasters does not have much: lich 47, gloom wraiths 48. Xivilai 45
Reason might be that their spells are powers and does not require magic.

Logically cheeps have 50 in magic, mudcrabs have 90, it makes perfectly sense that they have twice as much magic than liches.

Any npc will have twice their intelligence+ racial bonuses.
NPC daedra has lots of magic even the melee fighters a level 1 Dremora Churl has 324.

So your absorb magic sword would work nice against npc and npc daedra, but not so well against creatures, even the magic users would not be very cost effective. Might be an idea to carry two weapons one absorb magic for npc and one other against creatures absorb health would give symmetry and you would not need to waste magic or potions on healing yourself.
cast soultrap on selected monsters so you can recharge weapons.

The Atronach already forces your character to look for magicka in that way. Your RP might fall apart unless you come up with more background for your character's history. The only creatures that I can think of off the top of my head where you DO get magicka, are spriggans and will o the wisps.

I haven't really done the history much yet, but normally when I use the atronach, potions, telekinesis, and shrines are used to restore magicka. This time however, I plan on solely using absorb magicka enchantments, I don't plan on even using store-bought potions to restore magicka. Of course this means that I cannot be a pure mage type of character, I will also be using stealth and blades

He want to use a sword with absorb magic to take magic from non spell casting enemies to use in addition to the spell casting one, as I found it look like it would work very nice against npc and daedra, but not among monsters as they have little magic with the exception of mudcrabbs.

Ghosts have a nice reserve, along with necromancers, conjurers, and as stated above most npc's have nice enough magicka pool to leech from. If your going stealth then it would be awesome to roleplay this, an absorb magicka bow/blade as a secondary weapon would seem ideal. Use your power weapon for most the killing and wounding, and only switch to the magicka stealer after you can't cast detect life and chameleon anymore.... sounds like a fun idea man. Everything in the game that can cast a spell has magicka. It's not like you need to absorb all of it off of one guy, but occassionally you'll be lucky enough to come close. You will have over 200 magicka to start however, which is enough to cast all the support spells a stealthy adventurer would need in a single dungeon. I think your character won't have any trouble managing his magicka pool..... Besides.... who needs spells when you're fighting bears... LOL.