Cavs don't need to trade Love. He is going to miss a month and they weren't winning with him. There is no reason for them to trade him at this point (they can't trade him for awhile anyway). That said, the Cavs should absolutely be selling off any of the veterans that any team will take. I doubt they can move Smith, but Korver and to a lesser extent Hill probably have a market if they aren't looking for much in return (which they shouldn't be at this point).
I've been saying all summer the Lakers made a mistake in not getting Leonard because they were going to waste the best season that Lebron James has left. They need to make a move. If I were them, I'd make a real hard play for Beal. I think he would be an excellent #2 for them and as you say, the Wizards need to do something (and Wall and Beal always seem to clash and Wall is basically unmovable).
The Sixers are the other team that really should do something. They shouldn't ruin their cap space this summer (unless they a very good player, like say Beal), but they need to do something with their weird roster construction. Would the Wizards do Covington, Fultz, and Korkmaz/Shamet for Beal (as an example). I don't know if that is enough for Beal, but that nearly gets the Wizards out of the tax and gives them some depth, Covington/Porter/Morris is an interesting wing combination, and they get the shot that Fultz materializes into his talent.