Throughout "Immigrant Blues," our speaker keeps naming and renaming the immigrant experience. He gives it a grand total of six titles, and the fact that no single name seems to quite capture it suggests that this is pretty complicated stuff he's dealing with. Not only is his experience outside the norm of his country's culture, but it also seems to be outside the ability of any language to convey it. We might also consider our speaker's confusion about body and soul, and about his connection to his lover, as springing from a sense of being foreign even to himself and the woman he loves.
When our speaker declares that certain experiences or conversations are "the same old story," he is, in a way, making them less foreign. Things are foreign when they are new or unfamiliar. So if this story is old, then the experiences in that story are familiar and therefore not foreign at all.
Our speaker even feels disconnected from those who share a similar background, like his father and his son, because his status as an immigrant alienates him from everyone.