I have found that 5f5 paint remover is effective. It contains methylene chloride and is not to be confused with the one labeled 5f5 Eco Solve with which I have no experience.
Your job will be easier it you remove the doors to work on them.
If you have occasion to sand the surface after stripping you must be VERY CAREFUL around the edges of the veneered parts. If you let the sander go over the edge it will almost instantly go through all of the veneer down to the underlying core and be very apparent when you finish the part.
I find that the little "palm sanders" are very good. They use very small high speed random strokes and don't require any concern about direction relative to the grain of the wood. I have a Black and Decker model sold by WalMart and probably others that has its own little dust collector.
You need to use very fine paper and I would try to use 220 grit or finer aluminum oxide on the raw wood. I have found that powdered pumice with a multilayer pad of paper towel on the sander does a nice job if you want to polish the polyurethane finish between coats to get rid of the little blemishes, or after the final coat. You need to wipe the surface clean of particles before the next coat. I use Coleman fuel as a mineral spirit for cleaning up.