The best, and least harmful method of cleaning grease and oil soaked wood is one that's been around for at least 200 years.
The is the "whiting" method.
Buy a can of whiting (Calcium Carbonate) from Brownell's, or some drug stores.
Mix the whiting with a solvent to a pancake batter-like consistency and apply to the grips.
If your solvent is NON-inflammable, apply heat with a heat gun, or over an ELECTRIC stove burner.
The grease and filth will "boil" up out of the wood, and will be absorbed by the whiting. Brush off the dirty powder and re-apply. Usually two or three treatments will return absolutely BLACK wood to it's natural color.
The best solvent is trichloroethane, commonly called clorathane. This is a very slightly flammable solvent, and is one of the best grease solvents ever made. BUT, it's been determined to be hazardous, so it's hard to find.
You can use flammable solvents like MEK or even lacquer thinner, IF you use another technique.
Apply the whiting-solvent mix, wrap the wood tightly in a black plastic trash bag, and put out in the hot sun for a few hours.
On a rooftop works well.
Why whiting is so good is, many methods will bring the grease to the surface of the wood, but no matter HOW fast you wipe it, the grease isn't raised ABOVE the surface of the wood, and is reabsorbed back into the wood quicker than you can wipe.
With the whiting method, the grease is dissolved by the solvent and brought to the surface. The whiting absorbs the grease, wicking it up into the powder. The powder turns all colors of brown and orange from the oil and grease.
There are people who use dishwashers, oven cleaner, liquid soaps and other methods.
These all have the potential of damaging the wood, and worse, may leech back out later and corrode your gun.
Whiting has been used for a long time by stock makers and fine furniture makers to restore and clean wood, and it's proven to do so without damage.
Hey, many thanks dfariswheel for the information. I have a coupl'a old colts that were hidden or put up for years, wrapped in an oily rag or something as a preservative. Thanks for this very usable information..... Henri