FYI when you speak of Austria... you need to take into consideration... the fact that the Austria of 2004 is not the Austria that existed prior to the end of WW I, after 1918. Prior to 1918 Austria was part of the Habsburg Empire aka Austria-Hungary... which inc. all or parts of the modern countries of Austria, Hungary, Poland, Ukraine, Czech Rep, Slovakia, Russia, Roumania, Italy, Croatia, Slovenia, Bosnia and Serbia. So if your father's family emigrated prior to 1920ish then you may not find any info in present day Austria.
The place to begin is to determine where in "Austria" they were from, the exact village or town. Once you determine that then you may discover that there are records "readily" available for you... right where you live.
One purpose of this forum is to post queries regarding our ancestor search. There are people hereabouts who (at no charge because we enjoy the mystery and the hunt and helping others) may have some answers. You may in the end employ a "professional" but at least if you learn some basics about your family you will know if you are being given real facts of BS as sometimes happens!
Perhaps you may wish to get started this way, if so then you need answer the following:
1) Surname(s) and given name(s) of those who immigrated
2) Approximate year of immigration
3) Where did they settle when they immigrated
4) What was their ethnicity (FYI Austrian is not an ethnicity)
5) What language did they speak
6) What was their religion, this may help determine their area of origin
Best of luck with your project... I am sure you father will be pleased.
Croatian Heritage Museum