A lot of them are not exclusively Irish - I recall versions of nearly 20 of them from my childhood in Northwest Englnd in the 50s, so I guess you'd also find them in any country where English is spoken.

And a song doesn't have to originate in a country to become traditional there. I think some of Eric Bogle's songs are well on the way to becoming traditional in Ireland, while they're probably restricted to dedicated folkies here in England. And recent threads have proved that both the Wild Rover and the Black Velvet Band are originally English - but they are still traditional Irish songs now.(and English)