Mixing whiting with acetone to paste consistency and apply until the paste dries will draw some of the oil and stain out.I have found that by using a heat gun or hair drier,I can draw oil out and then flush off with acetone,but it Takes several applications and the best I can do is about 1/8" inch depth.I do not like to soak the stock in acetone.
I get the stock ready for finishing and then as a final step before I start,I flush again with acetone and let dry. If you let the stock set any length of time, you will see more oil migrating out.
Another reason to store firearms with the muzzle down.