Tuscaloosa: Dreamland Barbecue. There are/were two locations in town, but go to the original just south of I-20 to get the real feel. No menu, just ribs, sausage, and sliced white bread. This is good barbecue to folks who have never had Texas barbecue.
Starkville: Most network sports guys rave over Little Dooey's barbecue, but again - it ain't Texas barbecue, just a hole-in-the-wall with decent food and good prices. If you want something nicer, try Harvey's (the prime rib sandwich at lunch is damn good). For a really good burger and a cold draft beer in a fishbowl goblet, go to Oby's.
Oxford: Just walk around the Square and see what suits your fancy, as there is a broad range of decent options.
Never been to Knoxville, so I can't help you there.