From my understanding, and if I am wrong I'm sure someone with more experience and knowledge will correct me, only enchantress weapons increase the damage of our enchantress skills so the axe and sword will have no effect. The staff on the other hand should effect the damage of our skills, but I don't believe the skill description includes the additional damage, so to see it you need to do actual testing of the skills and look at the damage done.
Now, with that said, I don't understand why the Firestorm damage went down with the staff equipped considering it has a bonus to Int that the axe and sword do not. I defer to someone like Royce whose experience far exceeds my own on the subject.
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