To Kevbar, your father, Michael Anthony Barry, was my grandfather's brother, younger by 10 years. I went to Irishgengenealogu.ie, for the marriage certificate of John and Johanna and the three baptismal certificates of Mary, Heteona, and Patrick. I wonder about the spelling of "Heteona," but that's another issue. In the 1861 Census of Ontario, John and Johanna list their ages, I believe as 45 and 43, which would make their birth years as 1816 and 1819. Concerning "Patrick": as a witness to John and Johanna's wedding, I initially believed he might be an older sibling, but Irish naming patterns at the time (John named his first-born male Patrick) leads me to believe Patrick might has been his father, instead. If, and I haven't proven this yet, this is true, Daniel Harrington, whom I thought might be Johanna's older sibling, might also be her parent. Mary Glavin was identified by writing on a picture identifying her as Patrick's wife, but some words had been erased from that picture, and I'm not sure she belongs with Patrick. I think it more likely she was Bridget McCarthy's mother. I believe Heteona and Patrick were buried at sea, as family members told me.
In the meantime, I am chasing down John and Johanna's siblings (some came to Canada and actually lived across the road (almost literally) in Strathroy. I'm trying to learn more through the siblings. At the present time, Patrick and Daniel remain unproven as either siblings or parents. From what I have found, the John Barry and Judith Harrington don't fit. Barry and Harrington are Cork names and in the mid-1800s there were more Barry and Harrington families in Cork than in the rest of Ireland. I think we've also found mention of a Judy Harrington Barry in Strathroy, but it is likely another generation. I haven't pursued it because it's a little outside my interest.
I have been able to learn a lot from Canadian records, but Patrick and Daniel are still unknown qualtities.
If you find anything, let me know. I'm hoping to go to Ireland next year, spend some time in Co. Cork, and maybe have a professional see what he/she can discover. I have a couple friends in Cork City I plan to have a Guinness with as well. Keep in touch.