It isn't really set in stone, but I did go out of my way to define them once.
They all share the common attribute of being defined by rejection from mainstream society.
A Nerd is rejected or ostracized because he/she takes an interest in something or some things that mainstream society doesn't normally find interesing (math, science, history, etc.) However, these interests usually pay off as the nerd applies them to his or her career in the future.
A Dork is rejected because he takes on behavior that mainstream society finds unappealing (this can be anything from nonexistant social skills to unpleasant bodily habits).
A Dweeb isn't rejected, but rather attracts abuse because he makes himself look like an easy target for the maladjusted members of mainstream society who like to abuse dweebs.
You didn't mention this one, but there is also the Geek, who is rejected becuase he/she takes an interest in something that mainstream society sees as irrelevant to the real world (video game culture, particular movies, anime, etc.). While the mainstream viewer may also enjoy these activities, the geek tends to delve further into them than others are usually willing to. This one is most often mixed up with Nerd since they both revolve around strong interests in something. For example, a computer geek would be obsessed with computer games, while a computer nerd would be obsessed with how to build and program computers.
Anyway, that is my assessment of the Geek, Nerd, and Dork, terminology.