Both of the BF's questline usually takes a couple weeks.
To speed up the party questline, just keep raising your party popularity and you'll get a special decision when you're inside. This is usually done by succeeding the dance checks and, if you're a girl, performing exhibitionist acts or drinking the shakes when offered.
The clothes storyline will continue when the best friend asks you to help them study. I'm not sure what prerequisites you have to fulfill, but I usually get it maybe two to three weeks after losing my clothes.