This will sound bizarre... but does it smell like urine at all? Old urine?
I have heard of boys waking in the night needing to go to the bathroom, and using their closet instead. Really, I have a friend who has stories. Usually with younger kids, but.... any chance he sleep walks? Who knows what he is doing if he does..
And ditto the move the furniture and dig to the back of his closet. There is SOMETHING that needs thrown out and cleaned out. You just haven't found it yet. An old wet towel/washcloth or two somewhere even...
Could there be mold/mildew in his window or leaks anywhere?
ETA: I have an almost 14 yr old. I know that as they mature they start getting stinkier (no sweet smelling boys anymore at my house!)... but what you sound like you are describing is NOT just typical BO or hormonal changes, or sweating in the sheets.
IF it is his shoes, then vinegar soaks for his feet will help with the bacteria causing the smell.
The ONLY time my son's has ever had one of the rank smells you are describing (pungent, not just a general funky smell) was when there was something there. A wet towel. A wet bathing suit in the bottom of the hamper for a week. Urine in undies at the bottom of the hamper. When he was small-- urine in his toybox (yeah... not undies IN the toybox, just urine peed right into it. Over time it crystalizes... nice, huh?).
There is a specific source somewhere. You just have to find it. I'd check his dresser drawers for dirty things that may have been stuffed back in there when he was "cleaning" as well....
Good luck.
ETAA: Oh... and my DAUGHTER's room had a rank smell once last year. Turns out her TAG class had dressed up potatoes (cloth clothes and yarn hair even), named them, written about them and then let the students bring them home. Her potato was in a back corner of her dresser and was ROTTING. YUCK!