C&F, if it has just a small amount of old oil soaked in, heat will draw most of it out . You can use your oven to do it, if your wifey is agreeable.
Or, the heat lamp, as HG mentioned. If it is really oil soaked it is going to take a soak in acetone to remove it all, IMO. I have "salvaged" some really saturated buttstocks this way. Your can do a search for acetone/alcohol soak, and read probably pages about it. I think there may even be a "sticky" somewhere detailing it. Done properly it will remove all the oil. Some have said they have still had oil to come to the surface days later after the soaking ....... I haven't had that problem. It also should not require heavy sanding after drying, to get ready for the refinish.
Good luck, SRH