Just Hatched:
It all pivots on whether or not the paint on the wood is oil based or latex.
If it's latex, then I would use xylene to strip the latex paint off the wood. The xylene will etch the gloss of any varnish or polyurethane under the latex paint, but don't worry about that for now. Once you get ALL of the old latex paint off the old varnish with xylene, then just use a wiping polyurethane and give the trim a light coat with a brush roller or rag just to restore the gloss to the surface of the trim. (This is how I clean dry latex paint spatter off of varnished mahogany (really luaun) interior doors, but I have to apply wiping poly to the whole side of the door because otherwise you just get glossy spots where the wiping poly is, and that looks worse than the latex paint spatter.)
If it's older trim with real varnish on it, and if the first coat of paint on it was a linseed oil based paint, then you're SOL and you've got to strip the wood using chemicals or heat as InspectorD advises. You see, from a chemical standpoint, oil based paint and varnish are almost indistinguishable. Basically, real varnish can be considered "clear" linseed oil based paint, so there's no chemical that will dissolve one without also dissolving the other.
Quite honestly, if it wuz me, and you're planning to take all the old trim off to strip it with chemicals, I would just buy new oak trim to replace it. It'll cost a lot of money, but it'll save an awful lot of work.