Many hundreds (possibly thousands) of Irish songs were brought to the US following The Famine - largely as a result of the experiences of the immigrants back home and their reception in the US      
THese range from songs like 'Skibbereen' through to ones about being recruited to fight in the Army (Seven Irishmen)
A good place to search for Irish songs in America is the Helen Hartness Flanders site of New England songs
If you go further afield to Canada you will find many more
I embarked on a project to find Irish Child Ballads some years ago - Maine gave me some of my rarest examples
There are far more Ishish traditional songs that have found a home in America than there are that settled in England
Jim Carroll