Oven cleaner was mentioned as a product to use on oiled wood. It contains sodium hydroxide, also known as lye. Lye works the same as ammonia (ammonium hydroxide) because it will also saponify oils or fats and convert them to a water soluble soap.
Of course this must also be diluted and rinsed very well. Sodium hydroxide is used as part of the process to turn wood to pulp for paper making. Chemicals of any kind should be the last resort AFTER getting out all of the oil you can using heat and absorbent materials. Acetone, lacquer thinner, ammonia, lye, etc. can and will cause damage to the structure of wood if used incorrectly and for prolonged soaks. Even heat can be a problem if done incorrectly. I've told the story about splitting the forend of a Flues Ithaca while heating it in a microwave oven and wrapped in toilet tissue. Worked great until I got it too hot. It ain't glass or metal... it's wood... wood which may already have structural damage from decades of oil soaking. So we need to avoid cures that may weaken or eventually kill the patient.