IIWY, I'd try a substance known as "whiting". It's available from Brownell's, Midway USA and no doubt many others.
It's a powder which, when mixed with a solvent (usually acetone or mineral spirits) and brushed onto oil-soaked wood will "draw-out" and absorb oil, cosmoline, etc. as it dries.
Stockmakers and gunsmiths have used it for many decades.
Hope this is of help.