I used the console cheat to give msyelf every spell in the game just to see what they did. Obviously many of them are duplicate and testing spells, but some seem to work just fine and I wonder why I've never seen some of them. There was one spell that allowed you to turn health into magicka. There was the flaming wolf that charged into battle and blew up. There was the spell that let you turn a low level creature into a chicken. Lots of interesting stuff, but yet I've never seen a tome or a trainer that offered these. I had a mage up to level 40 who was the head of the college, but admittedly I quit shortly after that quest because I was tired of spell-casting. Maybe at that point some of the trainers would've offered me these?

Surely these can't all be quest reward spells, can they?

I don't know.... I don't really use magic. Early in game (until I get Fire Breath shout) I use Sparks off-hand. After that, I just don't bother.... I'm a fighter-oriented player, not much use for magic.

That chicken one sounds fun. I don't know but some of those are NPC only for sure. I agree there are a lot of spells I don't have but would like to.

Health-->Magicka = Equilibrium (Novice Alteration)
Flaming wolf = Conjure Flaming Familiar (Adept Conjuration)

Equilibrium and Flaming Familiar are quest spells.

The chicken one might be some random effect from the daedric staff.

...You get the spells after leveling up your character in the specific schools, and they're sold at the trainers.

A few others are retrieved via quests and whatnot.

I have no idea what you're talking about with the chicken one.

Chicken one could be Wabbajack testing in spell form, or maybe one of the training spells a girl from the College uses on you.