"Kazuki" for Takashi and "Papillon" for Mr. Shidou, from their resemblances to characters in Busou Renkin.
"Bitch" for Rei, which has been taken up even by her fans ("Bitch is cute~", "Nice, bitch"). Also "Roach" for her hair style.
"King of Braves" for Hirano. Also "Hirako" (平コウ)).
"Excalibar" for the crowbar Takashi uses at the end of Act 5.
Generally, "Awakening" (覚醒) (a Mobile Suit Gundam reference) whenever anyone gets their first moment of heroism/craziness.
Genius Bonus: Zeke is known as Zero in the official English dub. The Mitsubishi A6M Reisen fighter plane had the official reporting name of "Zeke" among the Allies, but it is far, far better known as the Zero.
It looks like some members of the Dai Gurren Brigade joined the fight against Them. Rei, Kohta, and Shizuka are voiced by Yoko, Viral, and Nia, respectively. Shidou is Kittan.
