"There's any number of methods, but the old time stockmaker and furniture maker method is the safest for the wood and most effective.
You'll need a good solvent, preferably non-inflammable. The best is Triclorathane, commonly known as Clorathane.
Also a jar of "whiting", which is Calcium Carbonate. This is a white, flour-like powder.
You can buy whiting from Brownell's and from many local drug stores.
The actual method depends on whether your solvent is inflammable or not.
Mix the solvent up with whiting until you have a pancake batter consistency.
Apply a thick coat of the solvent-whiting to the wood, including the butt area and the inletting.
Depending on how big the stock is you can coat it a section at a time.
IF the solvent is non-inflammable, apply heat with a heat gun, or hold the wood over an ELECTRIC stove burner.
The solvent will soak into the wood and dissolve the grease and oil, and the heat will cause it to "boil" to the surface, where it will be absorbed by the whiting.
Normal methods using solvents, soaps, or other chemicals can bring the grease to the surface, BUT they can't lift it ABOVE the surface.
As soon as the solvent evaporates or the heat is removed, the gunk is re-absorbed into the wood before you can wipe it off, no matter how fast you try.
The whiting actually wicks the oil out of the wood and absorbs it, where it's held. This turns the whiting orange and brown.
Simply wipe the dirty whiting off and re-apply.
Usually 2-3 applications will return even a black grease soaked stock to it's natural color.
If you don't have a non-inflammable solvent, apply the whiting with whatever solvent you do have, then quickly wrap the stock up tightly in a black plastic trash bag, and lay it on a driveway or roof top in direct sunlight on a hot day.
Allow to stand for a few hours, then unwrap, brush off the dirty whiting and re-apply.
This method is much less damaging to the wood than using dishwashers, oven cleaner, or strong liquid cleaners, and unlike them, there's no chemicals or moisture to leech out of the wood later and damage the gun metal."
Remember, you can't put something ON the wood, it also goes IN the wood.
What goes IN, comes OUT, sooner or later.
It's the "later" that can ruin a nice firearm.
Anything applied to wood will soak in, and at some point it leeches back out.
Sound like fun. Is that the stainless steel edition of the Ruger 10/22?