Welcome to JA!
A dork is similar to a "nerd" or "geek", but there are some subtle differences. A dork has strange or uncommon interests, which many/most people find odd or silly. Smart people are also sometimes called dorks.
Let me know if you have any questions,
Hehe, it's a mistaken belief that "dork" refers to the whale's penis.
No one truly knows where the word came from, but it's likely a from a form of "jerk" or "dolt". Or possibly because it sounds similar to "dick". However, I do not consider the word to be deragatory, since it can mean "smart" or "quirky". It really depends on the way your kids are using the word. If they are using it like "jerk", then your hang up makes sense. If they are using it for smart or quirky people, it's probably ok for them to use it. Context really matters in this case.
Here are some more "meanings":
My favorite is #4, and in my opinion that's the most accurate. But again, it's all about the context that you kids are using it in.