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1.
Possibly one of the greatest expressions ever. Used to show how much someone likes a concept or thing.

Synonyms include: Sweet, nice, kickass, all right, excellent, etc.
Mike - Dude, I got all the beer we need! Time to party!

Chris - Sweet shit!
by Definer October 13, 2004
 
2.
When something smells bad, as in a dumpster or outhouse, but has a tinge of something a little extra that's almost pleasant. Think of the smell when driving past a cow pasture or of rotting fruit in a garbage can full of trash or even a Honey Bucket that just had chemicals added to prolong the life of its use rather than empty it.
Me: "What's that smell? It's kinda bad..."
Him: "...but not really. It smells like... like... SWEET SHIT!"
by THE Mrs. Green October 22, 2010