Acetone will take finish off in a hurry. Getting old oil out of the wood that has soaked deep into the pores will take longer.
Laquer thinner works good too but doesn't evaporate nearly as quickly after it comes out of the soak.

Some people say a mix of the two together at the same time and then a separate soak of alcohol afterwards. They say it's great for oil soaked wood but I never had any better luck with it in the few trys with it than a pure acetone or L/Thinner soak.

The M16 rifle cleaning brushes ('toothbrush') makes a great scrub brush for cleaning up the gunk softened up but stuck in the checkering and crevices of the stocks or grips. *** DO NOT use a regular toothbrush-- it will disolve and melt in acetone and laquer thinner.

Pistol grips can be de-oiled pretty easily with acetone soak.

Gunstocks are another matter depending on the depth of the old stuff. I have a shotgun SxS stock I'm working on now that's gone through numerous soaks of both acetone & laquer thinner plus whiting applications and just when you think you've gotten it all,,it creeps back to the surface again after a couple of days.

I use the Zip-Lock freezer bags (heavyduty bags) to put the stock inside with the acetone. It doesn't use as much liquid that way as you can roll it up a bit and make the thing as small as needed for the stock inside.
They will not leak with acetone. They will NOT hold up with laquer thinner though and will start to leak at the seams after a few hours.