Here’s what church records exist for Omagh:
Church of Ireland:
Drumragh (St Columba) (Derry diocese)
Baptisms, 1801-1947; marriages, 1802-1950; marriage
notice books, 1905-26 and 1941- 84; burials, 1830-95
and 1904-74; vestry minutes,1792-1871, 1874-82 and
1894-1931; register of members, c.1880; marriage
notice books, 1905-26 and1941-84.
Omagh [Wesleyan Methodists]
Baptisms, 1832-1953; circuit schedule books, 1866-
1909; membership registers, 1863-1907; minutes
about rebuilding Omagh chapel, 1855-7; quarterly
meeting minute book, 1859-1902; circuit stewards’
book, 1829-85.
Baptisms, 1831-46.
Presbyterian:
1st Ballynahatty
Baptisms, 1843-1968; marriages, 1845-1936.
2nd Ballynahatty (or Creevan)
Baptisms, 1867-1984; marriages, 1846-1934.
Gillygooley
Baptisms, 1848-66 and 1869-1984; marriages, 1845-
1934; communcants’ roll, 1892-1918.
1st Omagh
Baptisms, 1856-1968; marriages, 1845-1927;
committee minutes, 1861-5; session minutes, 1874-
1913.
P. 2nd Omagh or Omagh Trinity
Baptisms, 1821-41 and 1849-1942; marriages, 1846-
1900; building committee minutes and accounts, 1855-
64 and 1866-70; communicants’ roll, 1896-1910.
Drumragh (Omagh) (Derry diocese)
Baptisms, marriages and deaths, 1846 and 1853-81;
index to baptisms, 1846-79; printed history of the
parish, mainly from the 17th century to c.1900.
The RC records are on-line on the nli site:
https://registers.nli.ieFor the others you probably need to go to PRONI (the public record office) in Belfast. A personal visit is required as they are not on-line there.