I started to play the PSP version this afternoon and i'll put all special mooves here when i'll get them.
first note; each character doesn't seems to have a special move with L button.
Hanyuu; oni wearpon plus kakera mode makes a powerfull mode in witch she gots a sword till she dies again (if you take the freezing power or the cat's gloves it will last till the jauges is empty, same with friendshipmode or oyashiro)
super ass hit, cat's gloves or freezing power plus any mode.
Mion; any mode plus any wearpon; press L when youre in hyper mode to get a super counter effect.
Natsumi any mode plus any wearpon, press L in hyper mode to give a serie of hits.
Mio , any wearpon set plus any mode, press L in hyper mode to do a poison area.
Kasai; super hit; any wearpon plus any mode.
Satoko same ( the super punch to make you fall of the brige)
Rena super punch ; first wearpon plus any mode.
axe hurrican ; axe or hammer toy plus any mode.
You have a first set with the story mode but you have to buy it afterwards.
For other costumes you have to play the battle mode till you got a batsugame for one of the fighters, then buy it.
For akasaka, and the angelmort costumes that you first can't find, when you get a batsugemu for that characters, you unluock thoses costumes XD.