Synthetic shoes, not leather? Try Febreze pet odor eliminator or similar strength deodorizer. That stuff is remarkably effective.
I don't have stinky feet or shoe problems, but with three cats, including one that's 15 or 16 now with a sensitive tummy and digestive and urinary tract problems, there's some occasional messy and stinky cleanup. I use a combination of Woolite or other fabric cleaners with enzymes designed to neutralize bad odors, followed by Febreze. Works great.
Also, try hydrogen peroxide. Very effective for stains, including blood from cuts and scrapes that get on light colored socks and jerseys, and many odors.
Don't use bleach, vinegar, ammonia, etc. Too strong, will damage the materials and may leave an equally bad and persistent odor.
For damp and mildewy or moldy leather or leatherette, I'd probably try a good clumping cat litter too. Something like Arm & Hammer Slide or Clump & Seal. These are the best I've found for cat litter boxes, and might help dry out damp, mildewed leather shoes as well, if nothing else works.