The hand gesture that Otonashi does when he asks this actually means/indicates 'gay' - sort of the Japanese equivalent of doing the limp-wrist thing.
Cue Otonashi asking 'Are you.' with a troubled look and an Aside Glance, and Hinata hurriedly cutting him off. Happens about once in every two episodes for Angel Beats!: Hinata will say something (such as 'I quite like you' or 'I need you!') that makes him sound like he has a crush on Otonashi.Amatsuki: In the manga Heihachi comes to the conclusion that Toki is hitting on him, and sadly recommends that Toki should be with Kon instead, as Kon is more good-looking.At one point, Lubbock snaps and yells, 'What is wrong with you!? Are you gay!?' Tatsumi denies it. Tatsumi is really shy and averts his eyes whenever they do this.
Lubbock is jealous of Tatsumi because all the girls fall for him and tease him with their bodies while they won't give Lubbock the time of day. All of a sudden some Yaoi Fangirls started squealing and having a fit. This happened to Ran when he was advancing on Mizuki.Akira looks like a girl at first glance however he uses 'ore', so people think he and his girlfriend Mizuki are gay lovers.