So I thought I would try leveling conjuration quickly by casting Soul Trap on dead bodies (corpses, animals) and, for some reason, I get absolutely NO exp from it?! I have no idea why, I do have mods installed but I do not understand why any mods would alter such a thing. Every mod I has is a popular one and I have not found any bugs related to mine on the forums/internet.

I believe this is actually a fix from Bethesda. You're required to be in combat to improve on the Conjuration skill. This is to avoid people from spamming it over and over and over and over to get level 100 on it.

Honestly, I really disagree with this 'fix' as it slightly limits the way people play, but hey, Bethesda is Bethesda and they usually make excellent choices with their game.

Ahh sweet man ahahah, do you think this is due to me having the "unofficial Skyrim patch"?

I can confirm that casting Soul Trap on a dead enemy still raises Conjuration in my game on the 360. Sounds like a mod issue to me.