Mmm, I've read this thread yesterday and been disappointed in lack of Rei love. Gonna fix that.
Maybe it's more obvious to me due to my personal interpretation of her character, but I really could see her singing in a band like
Crystal Castles or especially
The Birthday Massacre. If she had the chance to grow older, ethereal and deranged music could be just right way for Rei to explore herself. She could also become a singer songwriter and go all
Hannah Fury on us.
I could see Shinji on vocals in a band like
I Hate Myself.
In Asuka's case Either she would keep up her pretend art and be some kind of Eva equivalent of Britney Spears/Miley Cyrus (mental breakdown included). I REALLY could see her being famous for this overly sweet persona, and yet cursing and ridiculing her obsessive fanboys/girls behind closed doors. Or, just as Rei, Asuka could become an subversive singer-songwriter. She would be like
Emilie Autumn.
Hope that you won't mind me focusing on vocals - despite my love for music, I don't know much on how instruments work. For some reason, I can only see the main trio as faces of band. Asuka would probably hire some nameless dudes anyway.