ECB-054, starring Ayumu Sena has the best, out of place sounding opening theme. It also plays during the trailer, check it out!
No, actually, that honor goes to MIGD-676, starring Kurea Hasumi, which is going for something a lot more dramatic. Behold!!
Both PLA-057, starring AIKA, and HODV-21152, starring Ayumi Shinoda, are using the same catchy chiptune song for their intro. It's only playing during the latter movies' trailer though.
http://www.dmm.co.jp/litevideo/-/detail/=/cid=41hodv21152/ (Seriously, that tune is surprisingly good.)
PGD-883, starring Yui Hatano, has a pretty catchy...I guess you'd call it Vaporwave? Synthpop?...opening theme, but it doesn't play during the trailer. The trailer song is still kinda decent though.
But of course we all know the real winner is Ai Uehara performing the theme song to that one 100 dudes creampie movie she did for AV Open a couple of years ago. So bad it's good.
Special mention goes to ASW-117, starring Akari Hoshino, which uses samples from an old german rap/pop song from the mid-90s during both their trailer as well as during the full movie. Blows my mind.