If they're that bad try saturating in hydrogen peroxide. Pour it on liberally and let sit awhile. Then repeat. Should be okay for most synthetic shoes, and acceptable for many leather shoes if the only alternative is discarding them.
With the synthetic shoes, after dousing in hydrogen peroxide, fill a mop bucket with tepid water and a Tide or Gain gel fling. Best laundry detergent I've ever tried, reliably gets the funk out of my cycling and work clothes. Tide and Gain will get the mildew funk odor out where every other detergent I've tried failed. But the enzymes need time to work, so let 'em soak for up to 20-30 minutes for best results. Doesn't need constant agitation or scrubbing, just time.
I even dunk my Merrell cycling/walking shoes in a bucket of Tide/Gain every few months when wiping down the outside doesn't cut it anymore. So far, so good, no problems with glue or layers coming apart after a year's hard use.