The Public Record Office of Northern Ireland (PRONI) has an eCatalogue of documents which can be searched by entering the name (eg) of our clan. There are seven documents which may be of interest which I have listed below. The site doesn't indicate whether you can see the original, though presumably you can if you visit Belfast. You used to be able to ask PRONI to send you photocopies of originals, and I do have the first five listed below, and fascinating they are!
1. 16 June 1786 Assignment of the Mill Tenancy in old town of Larne. Consideration £8.0.0 John White, Larne, to James McElhago, Larne (PRONI ref: D300/2/1/97/21);
2. 1 Aug 1786 Lease of premises for 3 lives or 31 years from 1 Nov 1783. Consideration £188.8.131.52/2. Rent £1.10.2 James McElhago, Larne, Co, Ant. to Charles Buchanan, Ballyvallagh, Co.Ant., Larne, Co. Ant. (PRONI ref: D542/4);
3. 29 Nov 1822 Counterpart Lease from Arthur, Viscount Dungannon to James McIlhago, junior, of Ballytober, farmer, for 31 years of 10 acres in Ballytober, Island Magee, Co. Ant.. Annual Rent £16. Owes multure to the mill of Island Magee (PRONI ref: D788/721);
4. 20 Dec 1824 Counterpart Lease from Arthur, Viscount Dungannon to William McIlhago of Ballytober, farmer, for 31 years of 3 acres in Ballytober. Annual rent of £5. Labour services and multure to the mill of Island Magee (PRONI ref: D788/931);
5. 22 Dec 1824 Counterpart Lease from Arthur, Viscount Dungannon to Samuel McIlhago of Portmuck, farmer, for 31 years of 10 acres in Portmuck, Co. Antrim. Annual rent £12. Labour and multure to the mill of Island Magee (PRONI ref: D788/953);
6. 1938 Mr. W.J. McIlhagga. Claim against his former representative in Courtrai (Mr. Wilson) (PRONI ref: COM/62/1/686);
7. Dec 1950 Belfast Association of Engineers: printed lecture: "Dynamometers and The Measurement of Power" by D.S. McIlhagger, M.Sc., Ph.D., AMIEE. (PRONI ref: D2703/2/7) (also D4063/9/75).