A while back, I made a query here as to what glue would make the most invisible joint in stock repair. A couple guys responded that they would only use polyurethane glue on oil soaked wood. I haven't yet experimented with oil soaked wood to check bond strength so I wonder if it has better qualities in this application. I would still try to get most of the oil out and then do my repair fairly quickly before the really deeply soaked in oil migrated back to the surface. Polyurethane does make a very strong and fairly invisible joint in closely fitted work. Might be worth trying some on a junk stock. The major knock on it I can see is that it's messier and harder to clean up due to the foam out. It's not so hard to scrape/sand, etc. on the wood, but it gets on your hands, clamps, rubber tubing, everything.