When Kagami/Tsukasa walked into Kona-chan's room while she's watching anime, Kagami said "Oosu" and Tsukasa said "Meesu". This is supposed to be a reference to "鉄コン筋クリート" or "Tekkon Kinkreet" manga and anime movie. I haven't watched the series even though I wanted to, so I'm not sure but these seemed to be the catch serifu for the 2 main characters.
The Mecha anime with bishounen/shoujo Kona was watching is "機神大戦ギガンティック・フォーミュラ" or "Kishin Taisen Gigantic Formula". The song playing is the OP from the series, "United Force" by seiyuu/singer Kuribayashi Minami (rather catchy).