If the draft card references Przemysl, your ancestors were from present-day Poland. Sections of both Poland and Ukraine (collectively called Galicia) were part of the Austrian empire around the turn of the century and immigrants from there would have been listed as Austrian.

LDS has microfilmed quite a few records from Galicia (I'm in the process of looking into some for my Ukrainian research). The Polish national archives in Warsaw would also be a place to look. Check on the Polish boards here - folks may recognize the name as being from a specific town (even if the spelling is off, which happens a lot with E.European names "translated" to English anyhow). Knowing a specific town would be very helpful in your search, since most records from that time period are church/parish records.