I can offer some info about the McNulty and Murtagh surnames, and perhaps a suggestion about another place to look.
My grandmother, Anne Marie McNulty, was born in the parish of Killasser in eastern County Mayo, and the McNulty surname is very common there. In Irish, the surname McNulty is Mac an Ultaigh, which literally means “son of the Ulsterman” (Ultach = Ulsterman, and Ultaigh is the genitive case of the word), but it may simply refer to descent from the Ulaid (in ancient Ireland the Uluti tribe), a people for whom Ulster is named, which in remote times ruled most of the North of Ireland. According to MacLysaght’s “Surnames of Ireland”, the surname originated in Donegal (where McNulty's can still be found), and that is where the Mayo McNulty’s came from several centuries ago. Many people left Ulster for Mayo and Galway at the time of the plantation of Ulster by Protestants from Scotland and England. McNulty emigrants from Ulster are also known to have moved to Counties Louth and Meath. In Meath, they usually just use the name Nulty, which agrees with what Roger found in the Nulty record which he cited above. If the name was McNulty in your family, that may indicate that they were not from Meath after all.
You menitoned that Christopher McNulty may have married Bridget Murtagh in the US, so perhaps they did not know one another in Ireland, but if they did, that may also point to eastern Mayo. There were two Irish surnames (from unrelated families) which were both Anglicized as either Murtagh or Murtha. They were the surnames Ó Muircheartaigh ("descendant of the navigator") in Leinster and Mac Muircheartaigh ("son of the navigator") in Roscommon. Actually, there may have been three families, since the name was also found in Scotland, and brought from there to Ulster, where it was usually Anglicized as Murdoch. Either of the two Irish forms of the name could end up as Murtagh or Murtha, depending on how they were heard by whoever was writing out the Anglicized forms (Irish has a number of sounds which English speakers find hard to hear clearly, and there are also regional difference in pronunciation). Roscommon is just to the east of the part of Mayo where my grandmother lived, and there are in fact a number of Murtagh's in that part of Mayo, presumably from that Roscommon Murtagh "clan", and my grandfather's Gallagher family (in the neigboring parish of Killedan) intermarried several times with Murtagh's, both there and after emigrating to the St. Louis area in Missouri, where I have numerous distant Murtagh relatives. If Christopher and Bridget knew one another in Ireland, then that might point to an origin in eastern Mayo. Unfortunately, the parish records in eastern Mayo do not go as far back as they do in some other places, but there a few parishes there (such as Swibnford) with early records.
You may want to consider DNA testing to see whether you can locate your McNulty/Murtagh branch. I and several of my second and third cousins with Mayo roots have been tested, and some of us first located one another that way.
