If quirky is taken to mean different to the norm, then you could call anything by Jose Saramago quirky, although it's literary fiction rather than contemporary.
There are passages written from the perspective of a dog, conversations between the main character and his own common sense and some great internal monologue in many of his novels, which are pretty quirky indeed.
The concepts of the novels - what if you met your exact body-double (identical appearance, voice, even fingerprints) (The Double), what if an entire city turned blind (Blindness), what if everybody cast a blank vote in an election (Seeing), what if people suddenly stopped dying (Death at Intervals) - say it all.
They are all amazing reads if you like a little more philosophy and a little less plot, although Blindness has equal measures of both and is probably the best.