Researching several sources, including my hard-copy Dictionary of Slang and Euphemism and http://www.takeourword.com/Issue011.html

I would conclude this:

1. The word comes from the mid-1900’s, and we are not sure exactly how it started.

2. It is very unlikely it had anything to do with any body parts of a whale.

3. It is likely a combination of “dick” as a word for penis, and “dirk”, a word for dagger, which has also been used as a euphemism for penis.

It is pretty typical juvenile behavior to use this sort of off-color name calling for unpopular people.

Dork Origin

It is popularly asserted that the term originated as whalers’ occupational slang for the penis of a whale, and by transfer became an anatomical insult, undergoing subsequent generalization and amelioration to its present meaning. The current state of evidence suggests that this is a case of folk etymology[1], as no solid documentation has been advanced for the use of the term in this context. One of the earliest documented uses of the word “dork” is a 1961 publication (referencing 1953), in which the meaning is clearly penis, but with no particular reference to whales[2]. Instead, the term may be merely a minced oath variant of “dick”, a vulgar term for a human penis. Nonetheless, the origin of the whale-reference and its widespread credit remain unexplained, and the claimed derivation is best treated as unconfirmed.

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RE:
What is the origin of the word "dork"?
When did it come into common usage as the word we know it as today?

dork

“stupid person,” 1967, originally U.S. student slang, probably from earlier meaning “penis” (1964), itself probably an alteration of dick.

Online Etymology Dictionary, © 2001 Douglas Harper

To STEVE – the Yiddish term you’re thinking of is SCHMUCK or SHMUCK.

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It’s short for “by our Lady” which is swearing against the queen. It’s like saying g-d damned.

I think its is a Yiddish slang word for the dick, and you know how people borrow slang terms from foreign languages so they can still cuss w/o sounding vulgar….

My bad, I thought this was the term borrowed from Yiddish