Not all physics PhDs are nerds, no. But an awful lot of them are. It’s quite reasonable to have a handful of nerds who all work (roughly) together at a research institute, and who hang out together in their spare time.
And I’m pretty sure that (as of the early seasons, at least) Leonard and Sheldon are both research professors, and Raj is a postdoc. I’m not as familiar with engineers, so I’m not sure what Howard’s job title would be.
I think it likely that Sheldon had an IQ test that had a genius level score. His mother had him tested to make sure he wasn’t crazy, and since she let him live in the sinful world of physicists she must have checked to be sure he really was a genius. Being a genius just means you’ve received a score on a test which has controversial significance.
It may not be “true” in the “every genius is a nerd” sense. But have you ever even read about what goes on at Comic-Con? We smart people love that shit. If you sidle up to a “genius” and ask them “do you love sci-fi,” I think you’ve got a better than even chance of coming away with a yes.
There is also the episode, “The Luminous Fish Effect,” in which Sheldon loses his job. Once he turns his attention from science, his creativity shows forth in other areas. He “fixes” scrambled eggs, plans a bulk mail-order tampon company (and then glow-in-the-dark tampons), starts making ponchos, and of course, develops a fish night-light.
I had to check to make sure you weren’t talking about a former boss of mine. The woman is considered a genius by most people who know her, but she’s got the charm of a steamroller. Once she decides to grab a project and run with it, It Shall Be Done, but neither as quickly nor as well as if she was able to listen to minions more than once a year. Kind of a pity, really, as her work impacts thousands of people daily.