A couple of thoughts...
Street: As I said, having a player in a DL spot costs you nothing, so there's no harm in keeping him there unless you run out of DL spots. And when (if) he's healthy he's a good pitcher that can get you saves. Right now you only have two closers, and you can have up to four in your RP spots (you'll notice that is why Ripplin is whipping us all in the saves category so far). But having said all that, if you still don't want Street, well, I wouldn't have made that move, but I can allow it.
A-Rod: This I won't allow. He's a top-5 pick in every league and just dropping him would have an adverse affect on the competitive balance of the league. In fact, if you look at the Can't Cut List that is maintained by Yahoo (not me), you are not allowed to cut him. I can understand you not liking the guy, but you shouldn't just drop him for nothing. It will have a bad effect on your team, but more importantly it will give another team in the league an unfair advantage - as if they were given two first round picks in the draft.
With all that said, you absolutely should trade him if you don't want him. But you need to get a fair price for him. I will not allow him to be traded for a so-so pitcher, for instance. Again, he's a top-5 player, and you need to get either another top-5 player or a couple really good players to make the trade fair for the league.
By the way, I'm also interested in trading for him. My 3B's have been pretty bad so far this year. Other teams in the league should be interested in him as well. What I would suggest is that you email the entire league (since not everyone reads this thread) and offer him up to the highest bidder.
Big Papi: I had no problem with that drop. I think he's done.
As a final note (to everyone) - if you are considering dropping anyone who is a halfway decent player, you should find out if other people want to trade for him first. You can definitely make your team better that way.