Apparently some type of rodent has died inside a closet wall in my home. Is there anything I can do for the stench other than tearing holes in the walls to locate it?

Sorry, there is nothing that I know of that will help with the smell except time. When I was a kid I had a pet hamster crawl into the heating ductwork of a new house. The smell went on all the next winter until it stopped. Nothing short of taking the duct work apart would have worked.

You need to locate the dead animal and make a small hole and somehow remove it. OR just close the bedroom door to the room where the closet is and don't use the room for a few months.

Any of the professional products out there that takes nasty odors out of clothing, carpeting, etc won't work in your case.