Hello: yes it was quite common in Ireland to drop the O as then your name wasn't so irish and people found it easier to work under the british occupiers. Later after emigrating you see families who were proud of the O and irishness to regain it.
Ancestry has amazing records for the U.S. so you probably won't have any trouble finding those records. They are up to the 1930 Census, unlike any in the UK, Ireland and Canada.
Not sure about Auz.
You might be able to find Argentinian information onwww.familysearch.org
as it is an international source
I sometimes use www.cyndislist.com
when looking for resources for other countries.
At least you are looking for an Edward (not Patrick or John)
in the US and that should help somewhat.