If you want a truly casual cruise then Ocean Village or NCL are probably the best to try. Both have good teen facilities, although these can vary ship to ship. The benefit of these lines are that you won't have to eat somewhere different just to be casual, as everyone will be.
Royal Caribbean's Independence of the Seas is your answer, we have just cruised on her maiden voyage and she is fantastic. The facilities for teenagers are second to none. Although there are a few formal nights you are not forced to dress-up and there are many informal places to eat onboard.
Both NCL and Carnival have excellent older Teen Facilities.
On Ncl there are also Karaoke booths to hire for the evening. Thats on the Norwegian Jewel a beautiful Shi.
Royal Caribbean - Independence of the Seas.