Although the word itself has no fully-feesible meaning or definition, it is commonly used in conjunction with other social slang and usually said in an informal context.
The term is usually not associated with direct offense, rather it is most commonly used to describe a past or present event in a loose social environment.
"This assignment is next."
"Some next guy asked me for loose change."
1) Weird, out of place, odd, different
2) Confusing, nonsensical
Always said with emphasis, perhaps derived from something along the lines of "This is stupid...next!"
2) "Yo, guy, this math problem is NEXT"
God, I'm bitter.
"Dude, just next her, It's obvious she doesn't like you, and she just wants to fuck an outlaw biker. You screwed up, man. Just move on."
"No, I really think I'm in love this time, I'm mean she so pretty, and I think about her all the time... and blah blah blah blah"