Stains caused by oil can be dealt with in a number of ways, soaking in acetone is pretty effective.
If its in small localized places you can use a hair dryer and heat the area till the oil rises to the surface and wipe it off with tissue paper, repeating this over and over can work pretty well.
If i have had a stock in stripper to strip an old finish i often wash them with warm water and washing up liquid which can take a surprising amount of oil out the wood.
If it is oil staining on your stock i would make a bath of acetone and sit the stock in there for a good while and let it soak in. I sat a forend in a pint glass of white spirit while i went on holiday for a week and it turned the white spirit dark yellow with the eons of oil it pulled out so i know that can work too
The staining could be rust staining, which is where the tannin in the wood reacts with rust from the metal work around the inletting and essentially ebonizes the wood around the inletting, this is harder to remove really you will need to carefully bleach the wood to get that out; from my experience household bleach does not touch this kind of staining, there is a solution however that has been used for this kind of staining for years i just can't remember it!
I believe someone posted on the gunsmiths section on these forums with a solution they used which sounded similar to one i have read about but not used.
For removing staining in a non critical area ( not around the inletting!! ) working over the area area with courser paper might just get beyond it.
Just from my experience. - if i find that solution in my book i'll post it, its an old book on stock finishing.
Hope this might be of some help.
Edit to add:
http://www.doublegunshop.com/forums/ubbthreads.php?ubb=showflat&Number=425032#Post425032Covering the use of oxalic acid to bleach wood.
