I'd like to throw in my 2 pennies on some of the names mentioned:
Farnsworth - He'll probably get traded even if the Yankees are back in the race at the deadline. Like OgreBallz said, between the comments he made on the radio after Clemens was signed to him acting pissy when he was taken out of a game after allowing two baserunners in the same inning a few days ago, I think the Yankees are done with him. True he's making a lot of money for a middle reliever and still has another year on his contract, but he's quite tradeable.
Damon - Not going anywhere no matter what. He still has 2.5 years left on his contract. Any trade the Yankees could make for him would involve eating most of his contract and not getting much in return. He's worth more if they keep him and he can get healthy and produce.
Giambi - I'm sure the Yankees would want to trade him but there are two reasons why I don't think that would happen. A) He's hurt. Who knows when he'll be back. Probably August. If he comes back and has a strong last month and a half, his trade value gets a boost. B) Nobody knows what's going on with A-Rod. If he signs somewhere else, the Yankees almost need to keep Giambi because otherwise the lineup lacks a real power threat.
Matsui - I highly doubt he gets moved. Besides having a full no trade clause, he's been the least of the Yankees problems this year. Not to mention I'm sure he generates a good amount of money for the team (notice those Japanese ads in left field at the Stadium?)
Abreu - I wouldn't be absolutely shocked if he was traded, but I don't think he will. Maybe they could do what they did with Sheffield, pick up his option and trade him in the offseason. But the difference is last year the Yankees replaced Sheffield with Abreu in right field but they don't have anyone to replace Abreu. While the Yankees top hitting prospect is a RFer (Jose Tabata) he's only in A+ ball and won't be major league ready next year. The Yankees may just hold on to Abreu since the only good FA RF who could replace him is Ichiro, but Ichiro is on the wrong side of 30 and will probably get a 4 or 5 year contract from someone. I don't believe that Abreu has all of a sudden lost it. I think he'd be one of the top free agents this offseason so it would make sense to just keep him. I believe the free agent class after the 2008 season is quite good.
Clemens - Meh, seems pointless to trade him. They won't get a decent young player for him, they probably won't get anyone to eat much of his salary and he's not blocking anyone the Yankees have in the minors.
So that's my opinion for what it's worth. I don't think the Yankees will do too much at the deadline no matter where they are in the standings at that time. If they do some major retooling, I think it will be this winter and only after they know what A-Rod is going to do. Bad contracts or not, the lineup can't afford trading away their other bats if A-Rod walks.