There are three ways to explain the meaning of nerd, dork, and geek. The first one uses text only, and it is quite long. The second one uses a table (and it includes "normie"). The third one uses a Venn diagram (and it includes "dweeb").

Source for the definitions and examples: http://www.urbandictionary.com/define.php?term=Nerd
Source for the picture: https://laughingsquid.com/nerd-venn-diagram-geek-dork-or-dweeb/

• nerd
An 'individual', i.e. a person who does not conform to society's beliefs that all people should follow trends and do what their peers do. Often highly intelligent but socially rejected because of their obesssion with a given subject, usually computers. Unfortunately, nerds seem to have problems breeding, to the detriment of mankind as a whole.

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• dweeb
A dorky or nerdy person.
• dweeb
An awkward, ineffectual person; specifically connotes physical inadequacy
Ex.: Hey gang, let's go beat on the dweeb.
• dweeb
Different from nerd, geek, or dork. A dweeb is someone who is intellectual and socially inept, but also ineffectual and devoid of passion.
Ex.: Max, fitting the role of the dweeb, spent all Friday night reading Hartshorne's "Algebraic Geometry" while the others in the dorm wing went downtown for an evening of fun.

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• dork
Someone who has odd interests, and is often silly at times. A dork is also someone who can be themselves and not care what anyone thinks.
• dork
Someone who sits around, writing the 500th definition for a word in the Urban Dictionary, as if anyone will ever read them all.
Ex.: I'm such a dork for writing this.
• dork
A person who, although also socially awkward, doesn't have the intelligence to fill the void with technical pursuits, like a nerd, and is forced to do mindless activities. Almost always alone. Usually with an XBox. Like playing Halo. All day. Every day. Not even understanding how the Xbox is making the pretty pictures on the screen. Very sad.

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• geek
One of four titles used to classify someone based on their technical and social skills. The other three titles are nerd, dork, and normie. The difference between the four titles can be easily shown in table form:

Title	Technical Skills	Social Skills
----------	----------------	------------
Normie	......... No	............. Yes
Geek	........... Yes	............. Yes
Nerd	............ Yes	............. No
Dork	............ No	.............. No

Normie: A normal person.
Geek: An outwardly normal person who has taken the time to learn technical skills. Geeks have as normal a social life as anyone, and usually the only way to tell if someone is a geek is if they inform you of their skills.

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JJCC