How to clean and what finish to reapply depends entirely on the existing finish. If it is a natural wood finish, the odds are close to 100% that the finish is polyurethane....and usually a gloss urethane. You cannot put an oil on top of a urethane...the oil will just sit on the surface of the of the old urethane instead of penetrating the wood as it is designed to do. If you want to do it right and get a look-like-new appearance, do the following. Take the doors off, remove the hardware and lightly scour the door rails, stiles and raised panels using paint thinner and 4-0 steel wool. Rub with the grain of the wood. Then rub down with a soft cloth, let dry and apply a thin coat of gloss or semi-gloss polyurethane using a China bristle brush (use a good quality brush like Purdy). Do this also with the drawer fronts and the exposed cabinet frame facing. If the hardware is tarnished, try to clean with a polishing compound. If it doesn't clean up, replace the hardware. Then reassemble. I know, this may be more work than you had planned, but once finished, It will look like a new kitchen.