Yes they can, and yes they should.
They could file for slander, defamation of charater, and maybe a few other things.
Seriously, the DA and that stipper fucked up their lives pretty much for ever. They'll always be known as the duke rapists. They were placed up on a podium and hung out to dry in front of the whole country. The lawsuit would not be for the money, it would be more for the principle of the matter. And they should definitely go through with it.
Seriously it's complete bullshit what happened to those 3. There are a ton of rumors circulating that the DA actually forced charges on them, because he was up for re-election, and he is trying to win the black vote over.