It is very difficult. Is your father certain that his father was born to a Jewish family?
You could try to write to the current bearers of the name Waltersdorfer in Austria (see the phone directory I gave you the link to), and try to find whether they have a genealogist in the family who has collected data on the name.
Have you no relatives at all in the Waltersdorfer line? Your father needs to rack his brain for any geographical information he may remember from his father.