The HENRYS were a Presbyterian family in Clones parish, County Monaghan, in the early 1800s. Clones parish extended into Co. Fermanagh, and perhaps this is where your family's oral tradition meant they had lived.
In the Tithe Applotments, "Hugh Henry" was at Drumchunny townland, Magheraculmoney parish, Co. Fermanagh, in 1828. This may have been your ancestor, but you should check the Tithes index for Co. Monaghan as well. There were only a few Henrys living in Fermanagh at this time, and many many Gallaghers.
"Francis Henry" was baptising children at Stonebridge Presbyterian Church in Clones parish by 1824. His family had probably lived there for some years, since the HENRY name occurs at Creevlea townland at least 20 years earlier and perhaps had been there since the late 1700s. I haven't worked on the HENRYS as long as other families in that area.
Francis and Maria HENRY were counted as members of the Stonebridge Presbyterian congregation in an 1834 church visitation -- Creevlea townland: Francis & Maria Henry (with children) - Francis, Hugh, Margret, Bessy, Jane, and Maria. 3 males, 5 females, 1 testament.
There were several other HENRY families in Creevlea townland with my CALVIN/COLVIN ancestors.
Some of FRANCIS HENRY's children's baptisms were in the Stonebridge Presbyterian Church register, but marriage records there don't start until 1821-1822, so you'd have to look elsewhere for Francis Henry and Maria Gallagher's c. 1820 marriage. It might be at the earlier church in Clones -- St. Tighernach's Church of Ireland (some of this church register is available on LDS microfilm) -- or at a church in Co. Fermanagh. Stonebridge registers are on microfilm at the Public Record Office of Northern Ireland (PRONI) in Belfast.
Would be glad to trade more information if you'll contact me directly. I don't have any data on your particular HENRY families after they emigrated to Minnesota, except what I see in the Minnesota censuses, and would like to put them into family groups and see where they fit.