If all you've got is some gunked up lube and dust/dirt in the dies, then forget my first post and simply disassemble the dies and soak them in gasoline or some other solvent to loosen up and remove the grime.
If you've got some corrsion of the steel that needs removed or smoothed up then follow my first post.
First thing I do with any new set of dies, or any set of newly purchased used dies, is disassemble the dies, degrease in gasoline and swab inner surfaces clean, blow dry with compressed air, and then spray them with some corrosion protectant like a silicone spray, so they won't corrode and pit over time in storage.
I presumed you has some steel corroding with my initial response. Sorry if I got started in the wrong direction.