They shout, "I blacken the name of our fair city."
They also shout "Get thee hence, white trash," imitating a member of the socs.
Explanation:
When the boys are on their way to rumble, they show a kind of pride in being greases and start screaming and staging all the way, they sing and celebrate as a way to show their satisfaction with belonging to this group. They mostly shout a phrase common to all greasers that is "I blacken the name of our fair city."
They also shout "Get thee hence, white trash," imitating a member of the socs.