I've always thought of Scooter as being at least 17-18 when he first appeared on the Muppet show, at least in his last year of high school. Now I'd place his age at about his early twenties, 22-23 at the most. Old enough to be living on his own (or as "on your own" you can get at the boarding house) and to have matured a bit, but still young enough to have a lot of the same enthusiasm that he had when he was a teenager.
As for Statler and Waldorf, that answer is simple...they're older than dirt!
-Kim