Everybody uses these terms.
People use them interchangeably.
But in my mind they have distinct meanings.
First of all what unites them is that they all are subcategories of the greater category of social ineptness. All three terms have that common trait, some to a greater degree. But that is where the commonality ends.
Geeks are simply people who are defined by their obsession with particular activity, to the point where it causes harm to a more balanced social life. Nothing about being a geek means someone is inherently intelligent, nor are their pursuits generally intellectual in nature.
Nerds are a close relative of geeks, to make a geeky reference, nerds are to geeks, as Vulcans are to Romulans (if you are a male that wants to have sex, please don’t repeat that phrase unless you are at an event that ends in -con). But seriously folks, nerds by my definition are people that are extremely curious and spend much of their time excessively exploring an intellectual pursuit. In my mind an appropriate synonym would be a bookworm.
In summary so far, you would definitely want to cheat off a nerd’s exam in high school, but not a geek’s. If you were a stereotypical high school bully you want to punch both, which you could accomplish by going to the library. The former would be reading a book about the latest IEEE specification (look it up non-engineers), while the latter would be holding a 20 sided die, playing D&D.
And last (and also least) onward to dorkiness…
A simple definition of a dork is someone who is goofy, silly or quirky. An example of a dork might be the most socially inept person in an otherwise popular group of people. They may say inappropriate things, make bad or odd attempts at humor, but still have affable personalities. They like being social, they just suck at it. Dorks are also people who do not specialize in one particular activity. The other interesting thing about the term “dork” is that it is used more often to describe a type of activity as opposed to holistically labeling a person.
More recently, the terms “geek” and “nerd” have gained increasingly positive connotations, and have thus become more popular and a part of the mainstream, with the term “geek” becoming the most popular. There are now many variants of the term that have found their way into pop culture, such as the term “geek chic” referring to geeky clothing styles being incorporated into hip clothing brands and trends. But really the term has blossomed into describing a person as having a real passion for a particular activity. For instance phrases like, “I’m a real photography geek,” have come to mean that a person is passionate about a hobby but perhaps not a master of that hobby yet.
This is simply my take based on my generational and cultural influences. As with any word there can be many interpretations or connotations that vary by region and by person. I’d love to update this post, or write another in the future based on other people’s thoughts on the subject.