I think for Suigetsu, he wants to confront Kisame, and that's why he is traveling with Sasuke because Itachi and Kisame are partners.

For the girl, she just wants to ravage sasuke.

And the other dude, is helping sasuke because Kimimaro was the only one who could control his murderous rages, but now kimimaro is dead and sasuke is the only who could control him and make him stop hurting people.