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I would sand and remove all traces of existing paint and stay away from most over the counter solvents suchs as paint thinner, laquer thinner, etc.
More aggressive sovents such as MEK, Acetone, etc. would be a better choice; however, they are very dangerous to use...highly flammable, strong odor, etc. I would seek the help of a local contractor to chemically remove all traces of oil once you have sanded down to bare wood.