How do I remove wires that have been epoxied into place?

Spin the wire, but leave enough to grip with needle nose pliers.  Heat the other end with a lighter and pull with the pliers - in a few seconds the wire will slide out.  When the epoxy cools it will reharden without loss of strength.

The same things applies when you need to remove a screw that's been epoxied in.  Just head the head and back it out.