I've been an advocate of starting with absorbent materials such as kitty litter, whiting, or toilet paper using gentle heat to bring the bulk of the oil to the surface after first cleaning off any surface grunge with Dawn dish detergent. You can put the wood in a container of kitty litter and leave it in a vehicle parked in the sun for a week as a free long term heating source. I now try to minimize the use of strong organic solvents like acetone or lacquer thinner because wood is composed primarily of cellulose and lignin, and these solvents will break down those components of the wood. Doing nothing will also damage the wood, so you must get out what you can without causing more damage with long harsh organic solvent soaks.
After using the absorbent material to get most of the oil, I proceed to about a 50-50 solution of household ammonia and water. Strong ammonia should be diluted more. Ammonia will saponify both gun and skin oils, i.e., turn it into a water soluble soap. This must then be thoroughly rinsed off because ammonia will damage wood too. A soft scrub brush will help get out embedded grunge and dirt in the pores and in the checkering. After drying, if more oil needs removed, you can then soak in denatured alcohol before proceeding to the acetone or lacquer thinner, keeping those soaks short. This method also means there is much less oil to contaminate the more expensive solvents.
I don't believe you can ever get all of the oil out of a heavily oiled stock, and it will continue to migrate to the surface for months after cleaning. So it is best to do any glue repairs or finishing as soon as the wood is dry.
