Re: John, Peter & Patrick Harrington 1850-6
The Harringtons, father John b. 1824 and mother Kate Moylan, b. 1825, both Ireland, and sons John b. 1850, Peter b. 1851, Patrick b. 1856, Denis b. 1859 and Michael b. July 1862, all b. in Ireland, arrived in New York City on the ship Escort on 28 May 1863. An additional son Francis was b. in NYC in 1864.
Peter married Margaret Connelly, b. 1851, NY and Patrick married Rose Connelly, b. 1859, NY, there was also a Julia Connelly, and parents were Patrick Connelly b. 1833 and Anne Sweeney, b. 1830, both possibly Tipperary, Ireland.
As you note spellings were inconsistent and we have no info on any Massachusetts connections.