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1.
Feeling happy about someone else's misfortune. It's an English way of saying the German word schadenfreude.
I was so gleevil over the death of Osama bin Laden, that I listened to "Party in the USA" on repeat.

Perez Hilton is the gleevil Queen of all media.
by KayElleBee June 22, 2011
 
2.
A contraction of "gleeful" and "evil", describing a state of being where one feels joyously wicked.
1) A gleevil grin spread across his face as he thought about eating the last piece of pie without asking.

2) She gleevilly went about her business, happily crushing men's souls like paper cups.

3) The cat's gleevil demeanor concerned the old man - was Whiskers really trying to bump him off for the inheritance?
by dorkusmaximus March 03, 2009