Hi there,
Co. Clare has many parishes. Do you have any additional clue to where their exact place of origin might be? Have you checked family documents, such as letters and bibles, etc.?
Clare County Library has an excellent website where you should be able to find lots of useful links to County Clare. You can access it here: http://www.clarelibrary.ie/eolas/coclare/genealogy/genealog.htm
If and when you do find out an exact place of origin, I can then recommend some church records for you to check. In the meantime, there are other sources you can start looking at.
Civil registration records are available from the General Register Office (GRO). These start from 1864 however. You can access the website here: http://www.groireland.ie/research.htm
You could also try checking the land records called the Tithe Applotment Books (1823-38) or the later Griffith's Valuation (1848-64). Griffith's is freely available here: www.askaboutireland.com or here: www.failteromhat.com Failte Romhat has lots of other useful links you could try looking at. Tithe Applotment Books (1823-38). Microfilm copies of the books for all of Ireland are available at the National Archives of Ireland (NAI) http://www.nationalarchives.ie/genealogy1/genealogy-records/tithe-applotment-books-and-the-primary-griffith-valuation/ or the Church of Latter Day Saints (LDS).
Have you tried checking the Ellis Island records (www.ellisisland.org) or the Castle Garden records (www.castlegarden.org)? Generally, more information was given at the port of arrival rather than the port of departure. If you knew which city they arrived at, this could be a good place to find more information, and perhaps even find out an exact place of origin.
Have you tried checking for John's records in Ohio? There might be more clues there.
You might find this link about the name Eagan interesting: http://www.irishtimes.com/ancestor/surname/index.cfm?fuseaction=Go.&UserID=
Please make sure you link anyone else in your family who is interested in their Irish heritage to our site - and indeed anyone else you know of Irish heritage.
Kind regards,
Sinead Cooney
Genealogist (Ireland XO)