My grandmother, Anne Marie McNulty, was born in County Mayo in 1885. MacAnulty (when spelled with a "u" in the middle) is a variant form of the same surname (there are also several other variant forms). We're probably very distantly related, so I don't have info about your more immediate relatives, but I can offer you some info about the McNulty name and its origins.
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, as well as in Fermanagh), 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). A family of McNulty's migrated to the Callow Lakes area in Mayo in the 1640's, according to a history of the parish of Killasser, and thta is where my branch of the McNulty's lived (and still live - the name is still common in the area). The first parish priest of All Saints Church at Killasser was a McNulty.
There are also people named MacNalty or MacAnalty in Mayo (usally spelled with an "a" in the middle), but they’re generally from a different family, whose name comes from the Irish name Mac Conallta ("son of the wild hound"). Confusingly, they lived in the same area of Mayo as the McNulty's.
In any case, fáilte romhat sa mhuinitr! ["welcome to the fsamily"]
