Had this in a mid 1900's house. Or something that sounds very much like it.
Along with what others have recommended, I found that Ronstrip (or similar caustic soda type paste stripper[1] ) removed mine reasonably well, with the proviso that such stripper may raise the wood's grain.
[1] Made my own Ronstrip for the job from caustic soda (careful when adding that to water - it *can* blow up in your face as the act of dissolving caustic soda is *highly* exothermic. Go slow and check the temperature and wear goggles) and builder's lime. Not as good, but very cheap.Timbo