Carl,
Cleaning an old paint brush can be done with a chemical stripper. If it's a quality brush you should be able to restore it's usefulness. I don't think it's worth cleaning a cheap brush; it may fall apart. I don't think a good latex paint brush would be a good choice for varnish. Latex paints (all water-borne) are best applied with a synthetic bristle and oil based varnishes are better applied with a natual bristle.
I use a brush for only one type of finish; even if it could be used for more than one type.
e.g. varnish and shellac. I still don't share between finish types.
Scott
Finishing is an 'Art & a Science'. Actually, it is a process. You must understand the properties and tendencies of the finish you are using. You must know the proper steps and techniques, then you must execute them properly.