I've found out a huge amount more about him using some of the links on here.
In 1900, his birth date is out by one year - it should be Jan 1859, so one year out on year of immigration isn't too bad. BUT in 1910 he says he immigrated in 1896:
1910:
O William Moody, Chicago Ward 13, Cook, Illinois 50. Immigrated 1896. Widowed.
Florence E Moody, 28
Leroy William Moody, 20
Henery A Moody, 18
Minnie B Moody, 15
1920
Moody, Oliver W, Head, M, 60, W, - immigrated 1878
Moody, Leroy, Son, 30,
1930 - Chicago, Cook, Illinois
Oliver W Moody, 71
Age at marriage - 26
I've also got his obituary:
Oliver William Moody, a student of the career of Abraham Lincoln, died yesterday, the anniversary of Lincoln's birth. Mr. Moody, a retired painting contractor, died in Illinois Masonic hospital of complications which developed following injury in a fall last October. He was 81 years old, and lived at 3310 Harrison street. Born in London, England, Mr. Moody came to the United States at 17 and settled in Chicago at 27. Surviving are two daughters, Mrs. C. W. Jones of Highland Park and Mrs. Herbert Rosback of Elmhurst, and two sons, Le Roy and Harry Moody. Services will be held at 2:30 p.m. tomorrow in the chapel at 318 North Central avenue
Think I may also have found his great grandson on facebook!