Use whichbudget.com to search some of the lo-cost inter EU airlines that service the area that you want to fly. Using them you will see that you can use Air Berlin also for a flight between Rome and Vienna. My buddy who lives in Germany really likes flying with them...and their prices are great!
We have flown Air One and really enjoy them also. Personally, I would save Alitalia as a last resort.
But, you can go directly from Rome to Graz on Lufthansa, and they have some pretty good prices. Check out their web site.
Using whichbudget, you will see that Air Lingus has good flights and prices to Dublin from Vienna.