Are there JRI-Poland-like websites dedicated for Austria?
Try http://www.jewishgen.org/AustriaCzech/ausguide.htm, easily findable via Google.
You will find the birth records in the registers of the confessional institution since he was born before 1938 (the registration authorities started their work in 1938 in Austria afaik, see e.g. for Vienna here, but unfortunately German only: http://www.wien.gv.at/kultur/archiv/nutzung/forschung/personen.html)
In case he was roman catholic, you can contact the parish Deutschkreutz via mail: http://www.martinus.at/adressbuch/pfarre/27621042008143457.html or firstname.lastname@example.org
Ususally they will email you the requested documents.
The website to check is http://genteam.at, which has millions of records from Austria on its site. The problem is that European privacy laws prevent access to records as recent as 1931. However, there are people on the mailing list who may have access beyond what is available to you, and it might be worth asking a question on their mailing list.