My go-to for Thai cuisine in Memphis is Bhan Thai at 1324 Peabody in Midtown.
http://www.bhanthairestaurant.com/
As for Vietnamese, a quick Google search on "best vietnamese restaurants in memphis" came up with three hits, all in or near Midtown, that I've heard good things about (two I've been to and can give a good recommendation):
Pho Binh, 1615 Madison (been here and loved it)
Pho Saigon, 2946 Poplar (have yet to go--need to remedy that soon--but heard good things about it, and haven't heard anything bad)
Vietnam Restaurant, 74 N. Cleveland (I was there when they were located on Poplar (building torn down to put up a Kroger gas station), and it was good. I haven't been since they relocated to Cleveland, though).
Good luck!
Cheers,
bcg