The Show Using Nerd Stereotypes
There is no doubt that the show likes playing with the typical nerd personalities but claims that the show only handles a surface level understanding of geeks, nerds and everything in between is only a surface level understanding of how these characters are written and portrayed.
First off is that the vast majority of stories that feature nerds/geeks will use them in one of several ways. The first way is that they will be a deliberately secondary character; awkward, gangly and neurotic without a chance in hell of ever being considered cool by the main characters, the best you can hope for in their portrayal is that the main characters will at least acknowledge their usefulness and/or become friends with them. The second way is that if they are featured as the main character they will be a "cool geek" where the only thing that identifies them as a geek is some passing mention of a love of Star Wars or computers, they otherwise act like any other individual. The third way is the ladder climbing geek, where they do start out awkward and neurotic and learn how to shed that by either abandoning their geeky interests and personality or by gaining revenge on the bullies that resign them to their current status in life.
From there we can start examining the manner in which the characters on The Big Bang Theory are portrayed. These geeks are clearly the main characters, which takes out the first option. They decorate their homes with all sorts of geeky memorabilia, wear geeky clothing and struggle with navigating social situations, which takes out the second option. They have admitted to being bullied many times in the past and, on occasion, are bullied during the course of the show, but the show is not about how they "get revenge" on their tormentors. The few episodes where there they even try tend to end badly for them (several episodes regarding Penny's ex, an internet hacker and a few attempts at fighting back against Barry Kripke), which takes away the last option. Thus the show at its fundamental core is not the average geek-appeal story.
With that there are the individuals characters of the show. The primary focus of the show revolves around Leonard, Sheldon, Howard and Raj and as such they will be the primary focus of this analysis. Since the characters appear to embody certain stereotypes there is a need to address what stereotype they appear to be and then, using clear elements found in the show itself, show how they pick apart those character types.
Leonard at first appears to be the stereotype of the main character nerd who is actually very handsome, outgoing, friendly and socially capable despite all sorts of claims to the opposite. While that is where his Character Development is heading in actuality he is just about as awkward as the rest. He does fulfill The Everyman role of the group and provides the normal aspect for the rest of the characters to bounce off. Similarly, his awkwardness is less of a hindrance than the others because at worst he just has a hard time figuring out what to say, so when we watch him we are hoping he manages to find his words. This is evident enough in the pilot episode, when his lunch invite to Penny turned into a dietary advisement on a healthy colon.
Later on in the series we see and start to understand that he had a very unemotional and distant mother, one who expresses no pride in any of her children's accomplishments. This implies he craves emotional support in almost any form, which is certainly lacking in his friendship with Sheldon or any other friends. His initial attraction to Penny was obviously just an infatuation over a pretty face, but it grew out of their close proximity to each other and Penny's friendly demeanor (and willingness to hug him), which fed into his desire for someone to pay attention to him.
Sheldon seems to be the emotionless machine type of nerd, his only interests lie solely in his geekdom and science. His traditional role is the uber-nerd, the one trying to pull everyone else away from whatever scheme the others are hatching. The actual truth is that his child prodigy nature made him an outcast even in his own home, so his disinterest in social interaction comes from having no friends when he was younger and being forced to do certain things by his parents. He recognizes for the most part that he needs someone around to function properly, the least of which being him never getting his drivers license, and it is explicitly shown via a Flashback that before he was friends with Leonard he was even more quirky, anal and utilitarian in his lifestyle. Even now most everyone tolerates him along the lines of having bonded through Fire-Forged Friends and not because they have learned to appreciate all of his quirks.
His asexual behavior wasn't fully established in the early episodes, but it was made clear that his first love is science and his second love is his own personal geekdom, everything else falls far behind. Shipping being the way it is tried to pair up Sheldon with Penny based solely on the options of the cast and the comedic chemistry they had, but it makes sense that the only person who Sheldon might develop feelings for would have to be as extraordinary and peculiar as himself. It also isn't enough for Sheldon to have those feelings, but also needed someone who actually appreciated him for who he was, thus that is why Amy came into the picture.