A wedgie is when your undies get all bunched in between your butt cheeks, so therefore, a vagedie is when your undies get bunched up in your vajayjay, or your cookie. Very uncomfortable if i may say so myself...
*some guy goes and gives a girl a frontal wedgie* "OUCH! I have a major vagedgie now!!! It's ridin' way up there!"
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.