Some more experienced techs here can offer better details here I’m sure. From what I understand though, THHN is fine when fully inside conduit. If you’re not using conduit, you must use a cable with a properly rated jacket for the location it is run in. FPL can be run inside walls and ceilings, but not risers between floors or plenum areas. FPLR can be run in walls, ceilings, risers, but not plenum areas. FPLP can be run in walls, ceilings, risers, or plenum areas. It can also be exposed above 8 feet from the floor in places with open ceilings.
I have seen stranded wire in some places, but it is pretty rare in my area. Stranded is more prone to error as if a single strand touches the wrong place, you can accidentally send high voltage down a line and fry an entire circuit and panel. (Yes it has been done, not by me.) I’m not sure what the regulations say about stranded, but it doesn’t seem to be worth using in my opinion.