I doubt this song originated from Irish people. Irish people may mock many things about themselves, but the image of the 19th-century Irish - desperate, terrified people fleeing famine and humiliation, having at home been starved of education and unable to improve their homes or landholdings for fear of eviction by landlords who would use their improvements to get a higher rent, riddled by depression and desperate poverty, refused work because they were Irish, turning to crime as their only recourse, living in an internal society where often their only chance of rising out of poverty, endemic illness, constant danger of death and the bullying of the 'legal' and civil service forces that often acted as their enemies through prejudice, where a dangerous living might be made by bootlegging or gun-running or acting as the servants and messengers of those who had clawed their way up by way of pimping or serving the wants of the rich for illegal services - the idea that these people would find it amusing to mock the deriding image others held of them as dirty and drunken is risible.