This is an interesting question. Because of this question, I started giving Lydia all sorts of staffs that I found in my current game. She is using paralysis staff with great enthusiasm on top of the conjuration staffs and destruction staffs, so we will add that to our list. I took away chain lightening staff from her because it's an Area of Effect spell staff and it damages me all the time when she uses it. I gave her a healing staff, but she hasn't used it, yet. I'll give her a fear staff when I find one.
[Edit] I made the test more complete by giving Lydia a whole bunch of staffs I do not remember her using before and going through a couple of caves and bandit camps.
Alteration
- Staff of Magelight: No
- Staff of Paralysis: Yes
Conjuration:Banish
- Staff of Banishing: No
- Staff of Daedric Command: No
- Staff of Expulsion: No
Conjure:Conjure
- Staff of the Familiar: Yes
- Staff of the Flame Atronach
- Staff of the Frost Atronach: Yes
- Staff of the Storm Atronach
Conjuration:Reanimate
- Staff of Zombies: Yes
- Staff of Reanimation
- Staff of Revenants
- Staff of Dread Zombies
Conjuration: Soul Trap
- Staff of Soul Trapping: No
Destruction: Yes
Illusion: No
- Staff of Calm: No
- Grand Staff of Charming: No
- Staff of Fear: No
- Staff of Vanquishment: No
- Staff of Fury: No
- Staff of Frenzy: No
- Staff of Courage: No
- Staff of Inspiration: No
Restoration: Restore Health
- Staff of the Healing Hand: No
- Staff of Mending: No
Restoration: Turn Undead (Not tested yet)
- Grand Staff of Turning
- Grand Staff of Repulsion