There is no such thing as a language called Austrian. However, like many countries, they acquire languages throughout their history due to being so close to other big countries. The same can be said for Austria. Many of the people who live permanently in Austria probably speak German because it is the official language of Austria.
However, it is considered to be Austrian German which is different from the language spoken in Germany. Other languages include Turkish and Serbian based on the location of this country to the others. Some significant languages include Alemannic and Astro-Bavarian.
There are some regional dialects or languages including Slovene, Romani, Burgenland, Croatian, Czech, Hungarian and Slovak. Most likely groups of people move to Austria and bring their language with them.