Can I reapply polyurethane in small spots... or do I have to strip the whole thing and start fresh?

We just moved into our new house.... We have lovely oak cabinets... unfortunately the previous owner used pledge on them for 5 years (I dont know why people refuse to read instructions). They are covered with wax build up. We used Murphy's oil soap to clean them. It helped a great deal, but around the edges and scrolling it still has a layer of wax. If I sand the edges can i spot reapply the polyurethane or do I have to strip the whole cabinet door?

I would suggest trying an experiment on one edge. Clean it with mineral spirits or use wax and grease remover from a paint store. If the edge is grimy or soiled or if you just fell compelled to sand, rub the edge down with a fine grade of steel wool (going with the grain). I don't recommend sanding the wood because it may end up a different color. Then put on a couple thin layers of Minwax spray polyurethane. It blends in pretty well and comes in satin, gloss and semi-gloss. Rub with super fine steel wool or 320 grit sandpaper between coats.
If this works repeat it on the other edges. Avoid both the urge to spray on a thick coat and polyurethane that needs to be brushed on.
There may be another option that's feasible but I'm not that familiar with it. After the same preparation is done there are some oil finishes that can be rubbed on to worn areas. I've seen wood with several coats applied that looks lustrous and well protected.
Personally I'd go with the polyurethane since it's a known entity and it was good wear and water resistance characteristics.

Rub gently in the mouldings with white spirit & toothbrush.

Take the opportunity to strip the doors and add some new stain. Then coat them how you want. You will have re faced your cabinets in one weekends worth of work!
That's what I would do anyway.

You will have to remove the wax with a solvent before applying polyurethane. Poly will not stick to wax. You can apply urethane in small spots but it will probably show when dry. I would be cautious about sanding. The oak may only be a thin veneer that you do not want to sand through.