I'm a chemical engineer, albeit a little rusty. I'd sprinkle some corn starch on it and see how much oil that draws out of the wood. Let it sit for a while and brush it off. Repeat as needed several times (if it works).

I'd be leary of trying things like solvents or oven cleaner without testing them on scraps first. I think what they will do will be to spread the oil around, rather than remove it from the wood.