I'd be more inclined to be conservative, and only resort to acetone , lacquer thinner, etc. as a last resort. Wood is mainly composed of cellulose and lignin, and is structurally degraded by soaks in harsh organic solvents. It is a Catch 22 situation, because leaving the oil in the wood is also bad for it.
I typically start with stripping, and if the wood is oiled, I first like to use mild heat and absorbent materials such as kitty litter to bring as much oil as possible to the surface. This does take a long time, but you can really get a lot of oil out of the wood if you are patient. I then wash it with a solution of household ammonia and water. Ammonia will saponify the oil, i.e., convert it into a water soluble soap. This also removes a lot of old dirt and grime. Of course, the wood must then be rinsed well because ammonia can also damage wood if it is not removed. After drying, if it still seems oily, only then do I resort to relatively short solvent soaks. I then try to stain and/or finish fairly soon because I know more oil will eventually migrate to the surface. Getting thinned finish into the wood seems to stop this. As I said, I don't believe that you can ever get all of the oil out without damaging and degrading the wood.
