Hi darylr,
Sorry link to Ulster J. of Archaeology didn't work. I found item on LDS film #1279239 item 16. Think I transcribed all Farrells that I saw though. For good list of Kilmore Parish info you could try:
https://www.johngrenham.com/c_parish/c_parish_main.php?civilparishid=1965&civilparish=Kilmore&county=MonaghanI did see an Isaac Farrell listed in Kilmore Parish for Linen List of 1796 thru Grenham's site.
As to irregular marriages. Much of what was online seemed to deal with Scotland. For Ireland, it seems as if it was marriages that took place with out complying with legal requirements (banns/license) or "established social custom". Also apparently if a couple married outside of their home parish, or at the "wrong time" (perhaps Lent etc in the some denominations).
I found that marriage between a Presbyterian and a member of another denomination was not legal in Ireland until 1845. Maybe that was "irregular?"
Apparently these marriage may have been valid but sometimes they were "remarried" by Church of Ireland, (this also appears to be the case if they were married by a "defrocked" minister, cheaper & quicker and usually local).
In Scotland marriage could be by mutual agreement, or public promise followed by consumation, or by "cohabitation and repute".
Since Thomas & Agnes were married in Feb 1807 and 1st son John born April 1807, maybe the latter situation also applied in Ireland.
Anyway for what it's worth that's my thoughts on irregular marriage.
Maureen