As a surname, Nally is a form of McNally, which is from Gaelic Mac an Fhailghigh, which meant "son of the poor man". This is the explanation given in both MacLysaght's The Surnames of Ireland and Hanks & Hodges' Dictionary of Surnames.
Irish Names by O Corrain & Maguire has Irial as a form of Irél, a name from Irish legend (the son of "the great Ulster warrior Conall Cearnach"). Evidently no etymology is known beyond that.
This message was edited by the author on April 20, 2009 at 2:03 PM