From my understanding this is a pretty unique phenomenon in the Smokies. I know what you're talking about. One of the smells is a musky odor and the other is a sour odor and usually strongest in the fall. Skunks, bears, and hogs are often blamed but I can tell from personal hands-on experience that skunks and bears don't smell like that.
Rhododendron leaves supposedly give off a sour smell when they decay, especially in the fall when everything is nice and wet. The other is galax plant. It dies and starts to decay in the fall and releases a musky/sour odor. There's also a species of goldenrod only found in the mountains of NC and TN that emanates a musky odor, probably to attract pollinators, in the fall. But you'll probably only smell that one around the balds where it grows at high elevation. I think what you're smelling around the streams is rhododendron and galax.
I haven't investigated the smell myself when I've come across it but I've seen this discussed a number of times and those three plants seem to be the most likely culprits.
usually identified by later passing a wild, barefooted dread-head with enough body hair to make a yeti jealous.