Does it only affect Conjured Daedra that I've conjured? Or will it banish enemy daedra as well? Example: If im fighting some clown arch conjurer in a cave, and he summons his storm atronach, and i wack that atrnoach with my "banish" axe, will that storm atronach go away?

Yep, it banishes all summoned daedra that the level of enchantment will allow.