From your description my first guess would be stale towels and possibly even other items. Starting with the towels, if they don't dry out quickly after use they will go a kind of sour way and the smell is quite distinctive as well as being unpleasant. If used in that state the smell will transfer to the skin and, if washed at a low temperature, not rinsed really thoroughly and/or dried slowly, the transfer can reach other items too, particularly underwear and reappear as soon as the item is used.
The reason is that our skin sheds cells and excreted matter such as sweat and oils. These are digested by micro-organisms which proliferate in moist conditions - just the sort of washing/drying conditions I have described and in fabrics the organisms mature and die as well. This smell is particularly common around single live-alone young males, those who have not developed a rigorous routine regarding towels and laundry in general. Race and/or culture have nothing to do with it and I have most often come across it among "ordinary" white guys, simply because they are the type I most often move among. A single, long, hot wash of everything affected followed by multiple rinses will permanently clear the smell.
A small story: I once sat beside a young guy on a flight, we got into a conversation and he asked me if he smelled. I said no and he explained that he hadn't washed for many weeks (I seem to remember three months) because he had been on an expedition, he was deliberately going home without washing (for conversational effect ?). On reflection, I said, maybe he had a smell about him but I did not find it offensive or even bothersome, it was quite low level and struck me as natural. The point is that daily showers/baths are to an extent self-necessitating because the natural microbial balance on the skin is constantly being disrupted in favour of particular strains. They are more likely to be necessary, if only to cool down, in hot climates, not in northern Europe. Having showers resembling what is featured in films and advertising, whereby the water is constantly washing over people as they apply the soapy stuff (washing the soap straight down the drain) is a bit absurd, really just a rinse and not a wash. For a wash you turn off the water after wetting yourself, then soap yourself all over before rinsing - if not you might need to rinse daily or even twice a day in hot climates. I have always wondered at the habit found in places such as Australia, USA, etc. of going to bed sweaty, then showering (probably just rinsing) in the morning. Is the bed appealing after a night or two ?