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1.
The condition that a woman is in when she has a decent personality and/or sense of humor, but is most definitely not sexually attractive to men.

Derived from a combo of "Shrek" and "sexy". Shrek was cool to hang out with, but uglier than 10 miles of dirt road.
Mike: Jason told me that his new girl Sally was real sexy.
Tom: No way man! I've seen her firsthand and that girl is Shrexy. He's just in denial.
by Jay Smiff December 20, 2005
 
2.
The greatest compliment you can give to another human being. Surpasses "hot" and "beautiful". While the former words are used to compliment one's face and personality, "shrexy" means that you love each and every one of that person's layers.
The woman was not simply beautiful, or gorgeous, or any other one of those overrated so-called compliments. She was absolutely, and undeniably shrexy.
by Talia__ June 29, 2014
 
3.
sexyness comparable to shrek
How can u think she looks good? That bitch is shrexy!
by G Gritter February 19, 2008