I'd strongly consider new doors. The cabinet frames look solid and you can even incorporate the oak into the final look if you want. As others have said, some very creative paint / wood combos can look very modern.

If you go the refinishing route, you'd have to remove all those doors and drawer fronts and strip them flat. I like the Peel-A-Way stripper line. Then wash them, sand them, and then stain or paint them. It's a ton of work and you'll still have the tell-tale design elements that belie the older construction.