A lot of good advice from the posters here. I would add: He may not like this, but make sure he changes his socks at least once each day. Yep, two pairs (or more) of clean socks per day, at least until whatever is causing the stink is gone. One pair likely won't do it. Sounds like he might produce very heavy sweat and would need ot change out socks more than once daily.
You'll need to buy a ton of socks. Also make sure that they are 100 percent cotton or as close as you can get -- no spandex, no other materials IF possible. Again, he may complain that they "don't fit right" or sag at the top but 100 percent cotton breathes and the addition of other materials, especially anything latex based, makes them breathe a lot less.
Others have talked about cleaning his shoes but if it's as bad as you say, I would try to throw them out entirely and yes, as someone noted, he needs to have enough pairs of shoes that he is not wearing the same pair two days in a row, ever.
He probably does not even notice the stench so he may be resistant to these various cures, foot baths, throwing out beloved shoes, changing socks, etc., but find a way either to reward him for doing it or to give him an ultimatum if he doesn't. Sounds to me like a possible fungal infection and maybe he'll be willing to do something if he realizes other kids, especially girls, will smell him!
If there's a husband or significant other male at home, please, get that guy involved to take the lead on this. Your son is at an age where he may be very balky about mom getting involved in anything to do with his body; hearing all this from dad and having dad be the one to push the foot baths and clean socks etc. may make things easier.