Dear Fred uyI,
Thank you for sharing your situation with the Wefugee Community!
Unfortunately, I am not familiar with the Italian residence law. But I assume that your wife would need to have her habitual residence in Italy, if you want to apply for a residence permit there (That would be a requirement in Germany at least). If she lives in Austria, you might need to apply for a family reunification there. Please find details on the process in Austria here. It is in German language though, but I guess your wife speaks German?! However, according to the EU freedom of movement regulations, you will have in general the right to live together with your wife in the EU.
I hope this helps and please get back to us if any clarification is needed.
All the best,