I haven't a clue how to find the two in blue.
As for the others, my plan of attack would be to look for the names of the fathers in Griffith's Valuation, and hope you are right about them being from what is now N. Ireland, since that narrows things down to 6 counties.
In Griffith's Valuation of Ireland, (1850s-1860s) the surnames Henderson and McIlroy occur together in the same parish in many parishes in all 6 counties now in Northern Ireland.
from
https://www.johngrenham.com/surnames/So that looks pretty tough, but maybe the first name Archibald and occupation will help.
Was that side Protestant or Catholic?
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For Mullholland and McCormick, there might be a little more hope, assuming again they are in the North. The names occur together in the following parishes. I included Dublin, since these were
all the results for all Ireland, which does add weight to your thinking they were from the North:
McCormick Households
County Civil parish
Armagh Killevy 4
Derry Templemore 8
Derry Tamlaght O Crilly 2
Down Inishargy 1
Dublin Dalkey 2
Mulholland Households:
Armagh Killevy 1
Derry Templemore 1
Derry Tamlaght O Crilly 2
Down Inishargy 1
Dublin Dalkey 1
unfortunately on that side you have a John and Mary, common given names, and a farmer as well, which doesn't narrow it down at all.
However, you are just starting. A lot or most of the Irish records that are extant are online, unlike Austria, probably. And it might be doable.
Do you know if Bridget Henderson and her husband Patrick Mulholland were from the same place in Ireland? Sometimes, in the US at least, a person would marry someone from back home, at least in the generation that immigrated.