I'm playing Skyrim on PC and I've been having this glitch a lot lately. I've Google up "Conjuration battle axe glitch" to see if It's common and apparently it is since others are complaining of the same exact thing.
An addition to my finding.
http://www.uesp.net/wiki/Skyrim:Glitches
Occasionally when casting http://www.uesp.net/wiki/Skyrim:Bound_Axe, you may have no weapon or spells show up as equipped but will constantly have the animations of carrying the bound axe. You cannot draw any weapons or spells even if you change equipment, and cannot sheathe this phantom axe. This effect does not seem to wear off when the spell would have ended.
- Solution: Sitting down will take you out of the glitch.
- The issue appears to only arise when you cast in the third person view, so as long as you remember to switch to first person before casting you shouldn't have any problems (you can switch back to third person once the axe appears).
I just hope that this glitch gets patched because I'm unable to sit down while I'm battling enemies.