Ed, what did you use for stripping. Most strippers will take care of the old varnish or shellac or lacquer also. Because they have different solvents, you might test with wiping the brown gunk off with denatured alcohol or paint thinner/mineral spirits. Lacquer thinner would be the last choice since it doesn't sound like it is lacquer.
Remember that you will be dealing with flammable solvents and follow all the safety instructions on the labels. Be very careful with disposal of the rags too. Leave the rags outside and not folded or wadded up for 4-5 days to dry completely. You are safest if you don't consider bringing them in the house again.