Since this is a Jeep Wagoneer, are you talking about the fake wood stuff on the outside, aka Faux Woodie? If you are, the wood looking panel is a vinyl paper and the trim around it is plastic. Don't use anything too harsh to clean it. It's probably peeling in some places so you'll want to be careful. I'd just use your regular shampoo and wash mitt. Before you start working on the painted areas apply a generous coating of 303 to the whole area and let it sit. After you're done with polishing and waxing go back and inspect the wood stuff and if any areas seem dry, apply another coat of 303. Before you're finished with the whole job, go back and buff the wood stuff to remove any excess 303.
