I stay away from water immersion, I've had some issues with warping and ruined some wood that way. I use a home made steamer, and I degrease with varsol and FANTASTIC spray, or paint stripper if i'm refinishing the wood not just cleaning.
I will sometimes use a mild TSP solution (tri-sodium phosphate) on badly oil or grease soaked wood as a last resort, if i'm going to refinish the wood. It can have a bleaching effect on wood if you use too much.