Whenever I have to clean wood of grease or gunk, I start with acetone
and see if that removes whatever is on it.  It dries almost instantly
and leaves no residue and is a very good solvent.

The next material to try is a high purity alcohol.  Here I use
industrial 90% rubbing alcohol, but I have ready supplies of it from
work.  A good liquor store should stock a 90% alcohol that you can use.
If they don't work, use soap and water, then rinse it afterwards and
dry it with a towel.

Good luck!
Eli Shahar