This is a topic which is met with much debate because the book never identifies Oskar Schell directly with autism or Asperger's syndrome.  Speculation was made when the book was released because of the many character quirks Oskar displays which could easily be connected to signs of Asperger's.  First of all, he is highly intelligent for someone so young, and his intelligence manifests itself in a larger than life imagination and curiosity.  Some of his eccentric behaviors that may be specifically looked at in comparison to Asperger's include his sense of hyper-organization, quirky communication (especially with his grandmother), cursing, emotional outbursts, inventions, and the analytical way he goes about solving the mystery of the "Black" key, a mystery which he contrived.

According to the reviews, it is actually the recently produced film version of this book which directly links Oskar to Asperger's, mentioning that he was assessed by doctors but the diagnosis was inconclusive.  For autism/Asperger's awareness, this mention was huge.  Many critics are arguing however, that because such a detail was left ambiguous in the book, it should have remained ambiguous in the movie as well.