I would first strip off the finish. The let it set a few days and see how much oil migrates to the surface.
This will tell you how much was finish and how much soil soaked.
If oil soaked and there are the bad spots take whiting and mix a paste with acetone and apply over the obvious spots. Keep it wet for awhile. Then let it dry and brush off.Do this several times.
You can alternate using a heat gun or hair drier to pull oil to the surface and keep repeating the whiting paste or wash the oil of with acetone. You might have ot keep letting it set awile to see if more oil migrates to the surface.It is not a short term procedure.
Once you get as much oil out as you think you can and sanded as much as you want, wipe the stock with a wet rag and immediately dry it with propane torch, ( careful not scorch)sand with 320 or finer paper and repeat at least once more.
Use a sanding block so you are not sand ingaway thesoft spots and leaving the harder grain elevated
This will raise those whiskers.
Right before you are ready to start applying finish, wipe liberally withacetone and let dry, sand with extra fiepaer a, wiper withatack cloth and satrt applying finish
I don't like to soak in acetone as you still only get the top surface oil out.