Random bit of headcanon for Rei-kun and Kaworu living together says that at some point Kaworu asked if he (Rei) minded Kaworu foregoing clothes in the apartment, and Rei just looked at him like "so long as you put on pants before opening the front door for any reason I will completely not care what you do or do not wear". And the first time Shinji visits after that, he turns bright red over Kaworu walking around naked, and Kaworu just pouts, "Rei didn't say I had to put on clothes if other people came in," and Rei's just standing there watching his baby brother and his brother's not-boyfriend like, "I am not awake enough to deal with this."
Kaworu and Asuka are in friendly rivalry for Shinji. Who is oblivious. And yet somehow dating both of them, but they aren't dates.
Meanwhile, Rei (being asexual, demi-romantic) is amused by the whole thing, and very determined that Shinji make up his own mind about his love life.
"Please, nii-san, can't you just tell me which one you'd approve of more?"
"No."
"Please?"
"No! You need to decide this for yourself!"
"But--!"
"Shinji. I am not your father, I'm your brother. I'm not going to be disappointed in you for picking one or both or neither of them. What will make /you/ happy?"
The fact that Rei and Kaworu are living together already has people in school assuming they're either related or "living in sin", to which Kaworu is very confused and Rei just shakes his head at the idiocy. The only person who's opinion really matters to Rei is Shinji's, and Shinji knows what's up. The rest of the school can go hang.