The problem with most of the cleaning agents is they are very liquid and will soak into the cabinet. I am assuming the oil has left a sticky film on the bottom of the cabinet. What about Goo-Gone? I would try something with a minimum amount of liquid and move into something more liquid if the previous cleaner didn't work. If you make a mess out of the bottom of the cabinet you may be able to cut a piece of paneling to re-line the cabinet bottom. A cabinet shop may be able to remove and replace any parts.