Doing alot of SxS shotgun repair,,I've tried alot of different methods. I finally settled on soaking in laquer thinner for a couple of days first.
If you can get the wood into a heavy duty ziplock bag, it'll take much less thinner to cover it than in a pan. Plus it won't evaporate through any makeshift cover.
Test the plastic bag first with some thinner. Some hold up better than others and don't poke a hole in it!.
After a couple days of that, drag it out into the air and it'll dry in a few minutes or less.
Then I paint on a coating of whiting powder made into paste w/alcohol. You can use acetone or the Laq/thinner but they evaporate too fast for me and it's easier to get a nice coating on the wood when mixed with alcohol.
I got a big can of the whiting powder from Brownells years ago and am still using it up.
Hang the coated wood up for a few days to a week. The whiting will turn yellow/brown as the remaining oil weeps to the surface and is absorbed by the whiting powder. When it looks 'spent',,brush it off the wood with a paint brush & old toothbrush for the small areas.
Do this outside as the dust from the powder is like fine cement and will go everywhere.
Wear eye protection!
Recoat,,hang it up again and repeat till no more oil is pulled from the wood. Sometimes takes several coats. The oil can run a grain line and go completely through a stock side to side and deep in through the end grain in the inletting.
Yes it takes a while, but it's the only way to truely remove all of the oil.
Other quicky tricks, solutions, washings, etc get the surface and near surface oil. But after all your hard work of repair and refinish is done,,that down deep stuff will creep to the surface once again and push all your work aside.
It may take a few days, weeks or even a month,,but it will come to the surface as a natural path and push away any finish and weaken a newly glued repair.
Using oven cleaner does work,,but again it gets the surface and near surface oil.
It works by turning the oil to soap with the use of lye.
I have used it on stocks that don't have deep oil and that can also use the wood color evened up from stains, etc..
Now do a second treatment with wood bleach (oxalic acid).
It will nicely even up the color of the wood and lighten it a bit too after using the whiting powder de-oiling method. It leaves it very nice for staining and finish.
(This will neutralize the heavy base lye componenet in the oven cleaner if you used that method, though I don't really recommend it for deep, in the wood oil problems).
I do a quick dry with a propane torch to get rid of the surface water but let it hang and dry on it's own for a day or so after. Careful not to burn edges of inletting etc with a torch. It'll dry on it's own just as well.
Do Not use ordinary laundry bleach for the process. Wood bleach is available at Home Depot type stores in the paint and refinishing dept.s Mix the crystals with warm water and slosh it on. Rinse afterwards also.
Wear eye protection at a minimum when doing any of this stuff.