Starting in the early 1800s, freak shows were a popular form of entertainment that literally involved putting weirdness on display. People who had extreme medical conditions--obesity, dwarfism, hairiness--could work in freak shows while people paid money to gawk at them.
In the 1970s, the dance music hit "Le Freak" helped launch the disco craze, but also poked fun at the over-the-top devotion of nightclubbers.
Being called a "music freak" or a "computer freak" has a certain charm because the idea is that while you may be abnormally passionate about one special thing, you're probably very good at it. Like "Jesus freak," however, it also might contain a subtle putdown about being so fervent about something.
If you are not any of those kinds of freaks, maybe you are an average angsty teen like the TV kids on "Freaks and Geeks." Or maybe your freakiness just flares up once in a while without warning, like a freak snowstorm in summer.