If the oil or grease stain is fairly fresh on the wood, you may be able to remove it by scrubbing with an abrasive cleanser, such as Ajax or Comet.
But if the stain has been there for a while—for example, a can of motor oil that has leaked on a tabletop in a garage—this will probably not work.
Here’s how to remove the stain.
First, wipe several times with a fast-evaporating solvent such as acetone to wipe off the surface oil.
Then, mix a little of the acetone together with some fuller’s earth to make a paste. Fuller’s earth is available as kitty litter and is the material car mechanics use to spread on the floor to soak up oil and grease.
With either of these, grind it to a powder if it isn’t already powder. Then wet the affected area of the wood with the acetone and apply the paste of acetone and fuller’s earth over it. Let it dry back to powder and clean it off. You may have to do this several times. You should notice an improvement each time as the fuller’s earth sucks the oil or grease out of the wood.