I've cleaned several vintage tablecloths for people who bring them into the LYS. I've had luck with Ivory Snow and Soak. With Soak you don't have to rinse it. I always fill the bathtub just enough to cover the cloth with my oxyclean and Ivory Snow or Soak already dissolved in there.
As far as stains, Oxyclean usually works, but on two occasions, it's not done a thing. If your tablecloth is cream, the oxyclean will whiten it. It won't be cream any more. It doesn't seem to bother colors or ecru tho', which I think is strange.
When you take it out of the tub, carry it rolled in a towel so