You probably have been unable to find records as there are so few for Parish's in Antrim. The earlist RC is 1821 and only 1 CofI parish start 1788 and others not before 1807.
The RC records for Armagh 3 of 21 Parish's have early records most from 1814+. County Down is undergoing reconstruction so hopefully that means more records.
Finding passenger or shipping records that early is also close to impossible that early. Ancestry has an excellent collections but there are others.
If he married in the US then his marriage record would be in the US.
There are 47 McSherry's in the Northern Ireland telephone book, and at least two in Newry (Newbry?). The British telephone book comes with full addresses and postal codes.
I think this might be the only way to find someone to tell you where the family came from and where the ancestors are buried. You could see the 1901/11 Census www.census.nationalarchives.ie
to show you where the McSherry familes were living. Also the Grififith Valuation of 1862 (census substitute)will show you head of households at that timewww.askaboutireland.ie
The Tithe Applotment also for taxes is the earliest offical type records 1820-30's but as a single man I doubt your
John McSherry would be the occupant but the son of a McSherry in the Newry area. These are available at PRONI, the public records office in Belfast as well as on line with ancestry.com
You should check PRONI, for early parish records I believe they have them.
Newry is many things, it is a Parish in Armagh and a Union
also a townland and a town and is present also in Co. Down.
Too many for me to check. Go to the Griffith Valuation at www.askaboutireland.ie
and fill in just the surname and county (pick either) then look for the Poor Law Union of Newry. A Union covered an area of about 12 miles around the named town, parish's, villages, towns and townlands.
Since the name Newry was not in the Parish or townlands in any county you will be looking for the Union of Newry attached to a McSherry. Once you have boiled those down you will be left the closest possibilities to be his family.
Generally his children would reflect this father's name so Joseph maybe his father's name and Louis be his wife's father's name. There is no James listed in Griffith Valuation for all of Ireland, the father could very well be deceased by that time.
+ County (these resources have different amounts of information for each county, there maybe early parish records and perhaps the Tithe records.