Is tung oil a good product for natural oak cabinets?
It's possible-but-unlikely that there's nothing on them. Most likely they were done with a penetrating oil finish, - tung, walnut or linseed oils, or in the most minimal, least-color-changing but non-hardening realm, mineral oil. 

You could use any of those (use BOILED linseed oil inside, or else that never hardens, either) again, though linseed and tung may darken the finish a bit, or your could simply put a coat of paste wax on (I prefer "bowling alley wax" for non-floor purposes - it does not have the grit that some floor waxes do, and I prefer the clear to the "tinted" stuff, as well.) You can also mix walnut or boiled linseed oil with paste wax, rub on, rub off. Check the "look" of anything you intend to try on a surface like the inside of a cabinet door to make sure it works for you before you apply it to the whole face of the cabinets. 

Polyurethane will drastically change the look of the cabinets from a "more like raw wood" to "clear plastic coating over the wood" look. Whether that's good or bad is a matter of taste (and hard to go back from.)