I use three glues for repairs, and they have already been listed by the previous two posters. AcraGlass, thin-viscosity cyanoacrylate (CA) and medium-viscosity CA. "Satellite City" and "Zap" are two different brands of the same thing - cyanoacrylate glues from the R/C aircraft hobby trade. The thin stuff wicks into all those hairline cracks and stabilizes them, and also toughens "punky" wood by soaking into the grain and setting hard. I wick/soak it over the entire inletting to toughen the wood and oil-proof it. It can also be used to toughen up punky wood that wants to tear when checkering. The medium-viscosity is better when replacing a broken piece of inletting, etc., and structural repairs with a reasonably good fit that can be set instantly without the need for repositioning. The AcraGlass is for major structural repairs (like a broken wrist) where both sides of the joint are easily accessible and can be thoroughly coated without difficulty, and when a long set-time is desirable for positioning. Also use it to fill minor gaps where wood is missing in inletting, and for bedding the action to the stock for helping to prevent future cracks by providing an evenly distributed bearing surface for recoil and eliminating stress risers. All adhesives still require that you remove as much oil as possible from the wood before repairs. That said, these three seem to be fairly tolerant when you can't seem to get that last little bit of oil to come out.
