United needs three players for sure: an LB, a CB, and a playmaking CM.
For the defense, they need to get rid of Buttner, Vidic, Ferdinand. The best leftback they could realistically get is Fabio Coentrao, who if he could regain form, would actually be a superb signing. Another CB is needed, whether that be an experienced veteran (along the lines of Albiol, Subotic, Garay etc) or another, younger type. The CB doesn't necessarily have to be world class as I rate Phil Jones, but needs to be of sufficient quality as I'm not as convinced of Smalling and Evra.
In midfield, get rid of: Anderson, Young, Giggs, Nani. Buy a playmaking, action oriented CM who can comfortably alongside Carrick in a midfield two or Fellaini/Carrick in a midfield 3. This would be someone in the vein of Boateng, Guarin, Cabaye, though in the case of the former two they could rotate with Kagawa as the 10. I don't watch enough Bilbao to know if Herrera is this type of player or whether he is sufficient quality.
Play Januzaj as a guaranteed starter on one wing, play Valencia/Kagawa/Welbeck/Zaha as dictated by form on the other side. Cleverley is demoted to squaddie.
Strikers: Sell Rooney, give his playing time to Kagawa/Hernandez. Rooney will want out, doesn't take the best care of his body and will lose value quickly if they don't sell ASAP. Play a 4-2-3-1 from now on with VP at the point and Kagawa off him at the 10 where he excelled at Dortmund.
As for the playing style, they just need to put it on the ground a little more, and not play as much for crosses from Valencia. Their playing style isn't actually that crap, its just the missing players due to injury and the loss of form of certain players (Cleverley) which means they haven't been able to retain the ball as well as they should.