The reference to "Clanmarch" might refer to Clanmorris/Claremorris (in Irish, Clann Mhuiris or Clár Chlainne Mhuiris), which is some miles to the south of the Ballina area where you were looking. Claremorris is the name of both a barony (an older, not particularly useful division anymore) and an electoral division, as well as being the name of the main town in the area. This link gives a list of the townlands in the electoral division, along with further links to info on each of them:
https://www.townlands.ie/mayo/claremorris/
There's a little interactive map at that site which you can use to look around the area and see where Claremorris is located in relation to other parts of East Mayo.
Claremorris is in the Catholic parish of Kilcolman, and the parish records for there which are avaiable online can be found here:
https://registers.nli.ie/parishes/1056
Unfortunately, those records start for the most part in the mid-1830's (with a few earlier ones), so they may not be useful unless you can find more info.
I have both McNulty and Gallagher relatives from the area myself. My mother's parents were James Gallagher and Ann McNulty (so, the reverse of your family lines), who came from two different parishes north of Claremorris. Both surnames are found in Claremorris, but they appear to be far more numerous in the parishes just north of there. I've done a lot of genealogical research in the area, and traced my family lines back about 200 years, but unfortunately I don't have anything about your James McNulty and Catherine Gallagher in my records. Both names occur in my family, but James is a very common given name. Catherine is less common, in my experience, and one or more Catherine McNulty's acted as a baptismal sponsor in my family in the mid-1800's, but I don't know whether there's any connection to your Catherine (if she were already married when acting as a sponsor, the priest would probably have put her down as Catherine McNulty). I've done DNA testing, as have several of my Gallagher and McNulty second and third cousins, in case you want to compare results, but there were/are quite a few Gallagher's and McNulty's in the area (and some over the border in Sligo and Roscommon), so we may only be distantly related.
There is one Catholic parish in the nearby area with records which go further back than the others, and that is Swineford (also called Kilconduff). Those records are available at this link:
https://registers.nli.ie/parishes/0133
I mention that parish, because both Gallagher's and McNulty's are very numerous in that area (my grandparents come from the parishes just north and south of there, Killedan and Killasser).
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, a people for whom Ulster is named, which in remote times ruled the entirety of the North of Ireland. According to MacLysaght’s “Surnames of Ireland”, the McNulty surname originated in County Donegal, and that is where the Mayo McNulty’s came from. A family of McNulty's migrated to the Callow Lakes area in East Mayo (Killasser parish) in the 1640's, and in the course of time McNulty’s became numerous in the region. There are also still McNulty’s in Donegal and nearby counties, of course. McNulty emigrants from Ulster are also known to have moved to Counties Louth and Meath (in Meath, they usually just use the name Nulty).
There are also people in Mayo named MacNalty or MacAnalty, like that Peter McNalty whom you found. They’re generally from a different family, whose name comes from the Irish name Mac Conallta ("son of the wild hound").
Although the surname Gallagher is usually associated with County Donegal (where there are still many Gallagher’s), scholars now believe that a separate Gallagher "clan" originated in the Mayo/Galway area. In Irish, Gallagher is Ó Gallchobhair (modern Irish spelling Ó Gallchúir), and it means “descendant of the foreign help”, referring to a mercenary warrior brought in from Scotland or elsewhere in Ireland to fight in local wars (known as a gallóglach, or “gallowglass”). It may also refer to Norse ancestors, since the term "gall" was used for them as well (that is the root word in the name Galway (Gaillimh in Irish). Galway town was founded by the Vikings, and a DNA study a few years ago showed a significant percentage of Norse ancestry in Mayo and Galway. Although Gallagher and Gallaher are by far the most common anglicized forms of the name, especially in Mayo and Donegal, there are more than 20 other historical spellings.