I think you'll find that the Irish-registered aircraft are not owned by Alitalia but leased to it, usually by Irish-based aircraft lessors.
This isn't unique to Italy - for example in Russia a lot of leased aircraft are registered EI- or VP-B.
contrary to what en2r says, I don't believe that this is for flight duty reasons (Alitalia, Aeroflot etc don't have Irish AOCs after all!) but rather because in some jurisdictions, lessors find it legally easier to repossess foreign-registered aircraft in the event of a default by the airline.
And if you are an Irish-based leasing firm which owns an aircraft that's going to be leased to various carriers over its life, it's easier for you to keep it registered with your "local" CAA throughout its life.