If it's really oil soaked, and not just dirty externally, I don't think you have much choice but to remove the wood and get the oil out. Eventually, the wood will become soft and punky and much more prone to splitting from recoil. It isn't a very big deal to remove the wood on most guns.
I usually start with a scrubbing with household ammonia because ammonia will turn the oils into a soap which is water soluble. Rinse this mess off with plenty of hot water and allow the wood to dry before solvent soaking. This gets a lot of crud out in the beginning. By doing this first step with cheap ammonia, you get more mileage out of expensive solvents.
As PA24 notes, oil bleed can be a problem because the oil is often deeply impregnated into the wood. I've done some very bad ones with low oven heat with the wood wrapped in paper towels followed by solvent soaks until I thought the oil was gone. If I set the wood aside for several weeks and then get back to it for further repairs or refinishing, I sometimes find more oil has migrated to the surface. Because of this, I think it's best to do any crack glueing as quickly as possible after the solvent is evaporated.
