How do you get rid of foot odor?

Multiple pairs of shoes, so one or more pair can be drying out.  It's the cumulative effect that calls out the hazmat team IMO. 

Baking powder won't work. You want baking SODA; works best if he sprinkles it on his feet & between toes (or add it to a mint or lemon-scented lotion/gel/cream to massage into his feet).  Also, wool socks help; so does that thyme antibacterial spray sold at Whole Foods, but that could get expensive.

When I had this embarrassing problem, what fixed it was changing to cotton socks. It was the synthetics that seemed to create the odor. Go figure! A little bit of spandex or whatever doesn't seem to hurt. Good luck. 

You haven't listed what you currently do besides powder. That said, you want to keep the feet clean and dry, the shoes too.

If possible use breathable shoes or sandals, and make sure to rotate shoes. That will keep bacterial growth down. You can wash or line dry your shoes too. If your teen has a beloved pair they always wear, get two or three. If they will go barefoot whenever possible or use sandals that could help.

Always use fresh socks. Experiment with different fibers to see what works best.

Wash your feet, daily. Make sure to scrub off the old skin not just step into the shower. They can use something to dry out their feet too like hand sanatizer, deodorant (antiperspirant too), a salt bath, or powder.

If the odor is that bad I'd be tempted to throw out their current shoes and start from scratch.

He should wash his feet with hibiclens (over the counter). Leave it on for one minute and then rinse thoroughly. That will kill the bacteria.

You can try scrubbing the shoes with hibiclens too but maybe better to get new ones!

Seriously, try daily multi vitamins. We have a family member whose foot odor went away after starting a vitamin regimen.

I don't have foot odor, but I have massive underarm odor. I recently switched to Lavilin Aluminum-free Underarm Deodorant Cream - available at Sprouts, Whole Foods, health food stores, Amazon and it works for me - and I only apply it once a week! They make a foot cream called Lavilin Foot Deodorant Cream and I would bet it works too. Good luck.

Just a few ideas. Breathable natural fiber socks, no polyester. Lately my older son who has very sweaty feet, for whom cotton socks just don't work, has been liking wool socks. They breathe much better.  http://www.smartwool.com. Also more than one pair of shoes, so he can alternate them, and let them dry. I would also guess that his feet really need to air out, darkness and dampness lead to lots of bacterial and fungal growth. So barefoot time each day., especially in sunlight, when the weather permits. 

I make my son's stinky soccer cleats live out on our covered front porch, where they are safe from rain but are exposed to air and, more importantly, sunlight. That helps a lot. You might also try a tea tree oil foot soak, like the one from Purely Northwest, if you can get your teen to cooperate. I use it myself for toenail fungus, but I could imagine the tea tree oil might help against odor-causing bacteria as well.