Vonnegut is my favorite writer and I've been looking for similar stuff.
Catch-22 gets a lot of SH5 comparisons for a good reason. Similar themes and really funny.
Pynchon is a great postmodern writer, though more challenging than Vonnegut - maybe try Crying Of Lot 49.
Palahniuk is a more contemporary writer and a lot darker, but extremely good and has some fantastic prose. Fight Club is worth the hype. He was recommended to me by a fellow Vonnegut fan as the closest thing.
Fear And Loathing In Las Vegas is also amazing.
Have fun!