heres an example:

I use old nan (http://www.cardgamedb.com/forums/uploads/1281901798/med_gallery_17_192384.jpg) to give Eddard the house bolton trait. then I attach bloody scourge (http://www.cardgamedb.com/forums/uploads/1296004769/med_gallery_73_82487.jpg) to him. what happens next phase when eddard loses the bolton trait? I suppose he also loses the attachment, which is no longer legal yes?

while we're at it is it possible for a stark player to gain control (lets say with reek or dubious loyalty) of a character that says house X only?

Bloody Scourge is discarded: when you lose the trait you lose the requirement for bloody scourge to remain attached.

you can take control of an "house only" character: this is only a deckbuilding restriction.