Is it necessary to clean the enamel from enamelled wire before
soldering it?

I have a vague recollection that I read that it wasn't, and I only
have a couple little stubs that I'm afraid will beak off if I move
them around at all. (These are part of the 110volt winding in step
down transformer.)

Meirman-

There are some kinds of coating that burn off from the heat of a soldering
iron, but others are quite heat resistant. If the insulation won't burn off,
you will have to scrape it, use a chemical like Strip-X or use sandpaper. From
what you say, it will be delicate any way you go!

Consider that after soldering, long wires will exert forces on the stubs any
time they move. It would be a good idea to provide some kind of support like
a nearby terminal strip, that can buffer the mechanical forces of longer wires.

Fred