Austrian literature is a difficult category, as Austria waxed before and waned during the 20th century: wikipedia reflects the confusion. Vienna, an intellectual center to be envied in its days of empire, now seems just one amongst many mitteleurometropolises. Modern Austrian literature is identified with its brightest lights shining beyond its borders, Thomas Bernhard and Nobelaureate Elfride Jelinek (I've read and enjoyed a fair bit of the former, nothing of the latter as yet, and the LRB piece on Greed doesn't encourage me), with Peter Handke getting honorable mention.
But there's much more to it than that. Eurozine just released another in their series on European national literatures, "Literary perspectives: Austria: anything but a German appendix".
There are already threads established for Robert Musil (from the empire without qualities?), Stefan Zweig and Adalbert Stifter: who else deserves attention?