Betty Ann,
The second part of your query is about the Orr & McDole families. Firstly, I would say that McDole is an alternative for Madole and McDowell (which in Ireland is pronounced Madole). So bear those alternative spellings in mind in any research in the area.
You ask whether the names are common around Omagh. Omagh is a small town (Population 20,458 in the 2021 census). So yes the names will be common enough there, as they are across Ulster. Both are Scottish names brought here by Scots settlers. In the case of Orr that would be in the 1600s. In the case of McDowell/McDole etc, MacLysaght says it is a galloglass name, from the Hebrides but that additionally other McDowells arrived later. “It is now mainly found in north Ulster, largely due to more recent immigration.” Galloglass were Scots mercenaries hired by Irish chiefs to fight (whoever needed to be fought) in return for land in Ireland. They mostly arrived from Scotland in the period 1300 to 1500s. Their descendants today would usually be Roman Catholic. However the descendants of more recent arrivals from Scotland tend to be Protestant, either Presbyterian or Church of Ireland. Since your ancestors were apparently of one of those denominations, that suggests they arrived in the 1600s.
According to MacLysaght, MacDowell (and its variant spellings) is the Irish version of the Scottish MacDougall. In Irish and Scots Gaelic Mac Dubhghail means Black (dubh) Foreigner (gall). So, son of the black foreigner. Though it may sound surprising to someone unfamiliar with the language, MacDowell and MacDougall were originally both pronounced almost identically. Just spelled differently due to academics and others differing.
MacKenzie and McKinney were the same. McKinney is the Irish version of MacKenzie, and were originally both pronounced the same way (ie McKinney). Over the years the z in McKenzie has hardened. Gaelic has no Y and so scholars used the letter Z instead. That ultimately led to the pronunciation in Scotland changing, due to fewer speaking Gaelic, and so not understanding the correct pronunciation.
Omagh is in the parish of Drumragh. If you know your ancestors came from there, then there are 7 Protestant churches in the parish. None has any records for the 1700s. The Church of Ireland’s records start in 1801, Methodist in 1832, 1st Ballynahatty Presbyterian 1843, 2nd 1867, Gillygooley Presbyterian 1824, 1st Omagh Presbyterian 1856 & 2nd 1821. Copies of all those records are in PRONI in Belfast. There were plenty of churches operating in the Omagh area in the 1700s and earlier but they just don’t have any records for those times. No easy way round that.
You ask about information on where they left Ireland. There was generally no reason to record departure details in Ireland, and so there are no comprehensive records in Ireland that will help you. If they lived around Omagh and left around 1817/1818 then they may well have sailed from Londonderry/Derry. That was a popular departure port for folk from that area of Ulster but they might have sailed from other ports too. There were sailings from Sligo and some emigrants went across to Liverpool and sailed from there. There were many more sailings from England than from Ireland and competition for the business was fierce with agents often throwing the cost of the short passage to England in free as part of the package.
