Use boiled linseed oil, and you can mix in a small amount of mineral spirits or turpentine. It'll penetrate better. Soak the wood till it won't accept any more oil. After that, wipe off any excess oil. Soak again at least one more time and wipe off the excess.
It'll penetrate even better if the oil is heated, but do not heat over open flame. And then soak all rags in water and leave them wet, so they won't combust.