It looks like Mion and the killer were playing cards together. Someone got injured-- there was blood on the floor of the game room, though who was injured isn't very clear, because of the lack of injuries on Mion and people here.

The was a fight, but not in that room-- it carried into the art room, where Mion was knocked out and stabbed in the thigh. The killer wiped up the blood, and then made it look like she was hanged.

After that, they hid the sword in the incinerator.

I'm not sure how her room fits into this, but I think that's the order of events we're lookin' at.