I would also try using denatured alcohol first, which will remove any latex paint, but as far as any oil paint.......best of luck to you there. You might try lacquer thinner, but, as Jay suggested, try both in an inconspicous place first.
From a past expierence, I tried to remove paint from a floor laid in the early 50's. The old wax on the floor discolored when I tried both alcohol and lacquer thinner.