Update Jul 2016
I searched FamilySearch.org and found a death registration for Peter Neil so I ordered a copy. He died 24 Feb 1890 in St. Olave Southwark, London, England. The widow, Mary Neil, resided at 1 Woolf St. Bermondsey, London, England
In the 1901 England census I found Joseph Oneill listed as an inmate at St Joseph and St Anne Orphanage, Farnborough, sub-registration district Orpington, Kent, England. He was born at St Saviour, London, England abt 1888. I also found a Patrick Oneill born in London, England abt 1889 in the same orphanage.
Given the early death of their father in 1890, I assume, but have not proven the four boys were put into St. Joseph and St. Anne Orphanage. By the 1901 Census John and Peter would have both been over 16 and had already left the orphanage.
Peter married in 1909 in Ottawa, Ontario and raised a family of 7 children. Joseph and Patrick eventually ended up living in the South Porcupine area of Ontario and were miners. A few years ago I found an obituary for Paddy in a 1926 South Porcupine, ON newspaper. He was married with a 1 yr old daughter, Mary. Besides Peter and Joseph the obit also included the name of another surviving brother, John in Ireland, so at some point John left England and moved to Ireland. I found a John O'Neill in the British Army WW1 Service Records. He was in the Royal Irish Regiment, born abt 1879, married in Chapelizod Dublin on 5 Feb 1910, his residence was 15 Coombe St. Dublin and had two sons, John & Patrick. Don't know if this is the fourth brother, but dates & names seem right.
With all the information I had, including the many variants of the name O'Neill I sent for the birth record of Peter (my grandfather) and when it arrived he was listed as Peter Neal, but the parents were the right ones, Peter & Mary Neal, formerly Alexander. He was actually born on 2 Sept 1884 in London, England, not the 8 Sept 1886 in Ireland, as I believed.
Next I ordered the birth record of Joseph. I received it on June 30, 2016. He was listed as Joseph Niel , but the parents were again the right ones, Peter Niel and Mary Ann, formerly Alexander. Joseph was born on 14 Jan 1887, not 9 Feb 1886, as was on his military record.
On July 02, 2016 I ordered the birth record of Patrick. It has not yet arrived.
On July 08, 2016 I ordered the birth record of John. It also has not yet arrived, but from the 1881 census I know John was born abt. 1879/1880.
I've made a lot of headway this year, but there is still more to discover, such as finding John O'Neill's descendants in Ireland.