I spent about two hours today going from hardware store to box store as well as trolling the Internet to find an answer to my problem: dirty newel posts and hand railings. The floor refinishing people suggested we tackle these before we get the floors and stairs done (for obvious reasons) and recommended using a combination of a deglosser and paint thinner to basically clean them so they could then be refinished. After looking at the extremely noxious ingredients in these things I decided to try something recommended by This Old House instead.
Only using one noxious chemical, I mixed equal parts of Murphy's Oil Soap and paint thinner. You can see the results above. Maybe this is what I wanted - I'm not sure. I know that removing almost 90 years of grime is not easy but I also didn't want to have to strip the wood -- maybe I've already done that. Eek.