The only Warrington that I know of is in the United Kingdom. There is no Warrington in Ireland that I am aware of. The surname Hastry is also very unusual. Perhaps he was English? But married an Irish girl in Warrington. Lally and Glyn (or Glynn) are Irish names. Where did you hear of the Galway connection?
In Griffith's Valuation (1848-64), there are a couple of Hastry families - and both are in Co. Galway! http://www.askaboutireland.ie/griffith-valuation/index.xml?action=doNameSearch&familyname=hastry&firstname=First+Name&baronyname=&countyname=&unionname=&parishname=&Submit.x=0&Submit.y=0
And in the 1901 census here: http://www.census.nationalarchives.ie/search/results.jsp?census_year=1901&surname=hastry&firstname=&county=&townland=&ded=&age=&sex=&search=Search&relationToHead=&religion=&education=&occupation=&marriageStatus=&birthplace=&language=&deafdumb=&marriageYears=&childrenBorn=&childrenLiving=
Do you know where or when they were married?
If you know any more information, please add it to this message thread.
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). 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).
Until you know a more precise location, it is difficult for me to recommend other sources.
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.
Genealogist (Ireland XO)