Hi, ceilingfanrepair!
Unfortunately, other than the Crafts forum topic area, Furniture is about as close as we get here to post things concerning woodworking and carpentry. Might be room for one or two more topic areas...
My first thought on the removal of the adheasive substances would be to use heat, like from a heat gun, to make them softer so that a very sharp wood chisel could be used to cut and scrape or maybe use a single edge razor blade for cutting. Softening them should also help with the removal of any wood pieces that are joined together by them.
Thanks!