The best way of them all of cleaning oil from wood is the time tested old furniture and gunsmith's method..... "Whiting".
Whiting is actually calcium carbonate, a very fine, flour-like powder.
It works better than any other, and has the advantage of NOT damaging the wood like so many of the newer "expedient" methods do.
Unlike the other's, there's no chemicals or moisture to leech out of the wood later and corrode your gun under the wood.
One pound will do a number of stocks.
Whiting can be bought at many drugstores or chemical supply houses, or ordered from Brownell's.
How to use depends on what type of solvent you've got.
In the past we used Trichloroethane, commonly called clorathane.
This was an incredible grease-cutting solvent, nominally non-inflammable, but was found to be hazardous.
You may still be able to find it at some local oil companies.
To use, mix the solvent with whiting to the consistency of pancake batter.
Apply a coat to the stock, a portion at a time, INCLUDING the inletting and end grain of the butt.
Apply heat with a heat gun or heat lamp, being careful NOT to over heat and scorch the wood.
The solvent soaks into the wood and dissolves the grease and oil.
The heat makes it all bubble to the surface, where it's wicked up and held by the whiting.
The whiting turns all colors of brown and orange with the gunk.
Brush off the dirty whiting with a brush and repeat.
Usually 3-4 treatments will be enough to return a BLACK stock to it's natural color.
If you don't have a non-inflammable solvent, you have to alter the treatment, since a heat lamp or gun will be impossible due to the fire hazard.
To do it with a flammable solvent like lacquer thinner, mix the solvent and whiting, and quickly slob a coat over the entire stock, including the inletting.
Quickly wrap the stock tightly in a black plastic trash bag, and put it on a hot driveway or rooftop in the direct summer sun.
Let stand for the day, then unwrap, allow any remaining solvent to evaporate, then brush off and repeat as many times as needed.
Unlike other methods using liquid cleaners or oven cleaners, the whiting actually absorbs and holds the solvent and grease.
Other method may bring the crud to the surface, but they can't lift it ABOVE the surface where it can be wiped off.
As soon as you remove the heat, or the solvent rises to the surface, the grease is reabsorbed back into the wood faster than it can be wiped off.
While the whiting method isn't as fast and no-work as using oven cleaner, Simply Green or a dishwasher, it does do a better job than any of them, won't harm the wood, and won't leave chemicals to leech out later and rust your gun under the wood.