I agree, there were no thrift stores back then, except church sales that would sell clothes of seniors who had died (I was there at the time!)
Not to make this a history lesson, but back then clothes weren't made in mass quantities in China, they were expensive, well made in America, and in comparison to now, hard to find. People didn't fake their identity, either. If your sweatshirt said Yale, it meant you went to Yale. And most people dressed nicely wherever they went, unless they were literally alcoholics living in the street, and those were very rare, or self-declared hippies, deliberately defying social norms with their messy, dirty clothing.
People might buy a van for a trip to where it was cooler, but I can't see anyone sleeping in a van in the southern US in August, even now. Fewer vehicles had air conditioning then, too.
In the other hand, motels and diners were cheap and plentiful.
IMO, not wearing underwear could just mean they had a bag of laundry that they were planning to run through a laundromat at their next stop...another thing I recall both me and my boyfriend doing a few years later.
I believe this was a carjacking, and that very likely they did pickup one or a pair of ruthless hitch-hikers, who stole their vehicle, their id and money, and all their other stuff.
The only problem was, they weren't in sufficiently close touch with anyone as they travelled, so there was no one to know that they hadn't arrived somewhere, and had been travelling through South Carolina to get there. Again, no internet back then. When they didn't get back in touch, each individual friend or family member would assume it was by choice, rather than assume they'd been murdered.