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You will likely need church records to trace these ancestors.
It’s worth understanding a little about Methodism’s origins. John Wesley (a Church of England Minister) wanted Methodism to supplement the teachings of the Church of England/Ireland. He originally advised holding services on Sunday afternoon, so the congregation could still attend the Church of England/Ireland in the morning. He didn’t want it to be a separate denomination, though eventually it did become one.
Methodism took a lot longer to become established in Ireland as a separate denomination than in England. In Ireland there was considerable resistance to separating from the Church of Ireland. In 1816 the main body of Irish Methodists (the Wesleyans) took the decision to allow baptisms in their preaching houses or chapels, but it was a practice that was only gradually introduced so that it wasn’t until the 1830s or 1840s that it became fairly standard. Because of continuing loyalty and other factors, many - including Primitive Wesleyans - continued to use the Church of Ireland for years after this and it was 1871 before all Methodists routinely performed their own baptisms.
For Methodist marriages, the earliest I am aware of date from 1835 (Belfast Donegall Square, the first Methodist church in Ireland). However in the mid 1800s there were only a few Methodist Ministers (Methodism relied heavily on lay preachers). That shortage led to the continuing practice of marrying in the Church of Ireland. In addition, in the early years, many Methodist Meeting Houses were not licensed for marriages so that too contributed to marrying in the Church of Ireland.
So to summarise, you are unlikely to find many Methodist baptisms before 1829. Few marriages before 1840s and only a handful for many years after that. If there are no Methodist records in the location you are researching, try the Church of Ireland records instead as that’s the most likely place to find them.
Not many Methodist Meeting Houses have graveyards and so many are buried in public or Church of Ireland graveyards instead.
In Mohill’s case the local Methodist church has no records earlier than 1882 suggesting that the congregation used the Church of Ireland for baptisms and marriages until then. Mohill Church of Ireland has baptism, marriage and burial records from around 1785 onwards. My guide to church records says they are in the RCB Library in Dublin, and that some years are also on the Rootsireland site (subscription).
NON RC marriages were recorded in the statutory Irish marriage records from 1845 onwards. I did search for Ann's marriage to James Woods 1845-1865 but did not find it.