Not sure which Ernest Oswald you mean, but:-
Ernest Charles OSWALD born 1881 was born in 1881 in Birmingham England. His parents were: John Robert OSWALD 1855-1940 and Caroline HORWOOD 1854-1926. I am not sure where and when he died, or
Ernest OSWALD 1907-1980 was born and died in Birmingham England. His parents were: William Edward OSWALD 1878-1952 and Nellie TINSLEY 1877-942.
Neither to my knowledge emigrated from England.