This term originated through the use of scat, or nonsensical language. It is meant to be pronounced in a very loud and high pitch tone of voice with particular emphasis on the "wee" part of the word when one articulates it. It also works best when an individual is enduring a barrage of stress in that particular moment. Therefore, the word, when used correctly, relieves stress.
Alex: "Hey Kristy, how're you doing today?"
Kristy: "Not too well. I hate school and work! I just want to scream!"
Alex: "Have you tried the Aweeka method?"
Kristy: "Tried it?! I live by it! AwEEEEEEEEEEEEEEEEEEEEEEEEEka!"
It is said of the situation where a person has the bad luck to make contact with his testicles against an undefined surface or object, intentioned or not.
Given the nature of the word, it is more appropriate to design cases where the interaction is made with a moving object, for example, a ball.
Although it is extremely painful for the victim, it tends to be considerably funny to people who witness it.
Today in the baseball game the pitcher took a nutshot; the baseball hit him in the nuts.
Man, I just watched the funniest nutshot video ever.