For the most part, the song is straightforward love song, the narrator declaring his feelings for Eileen. But the first verse is about Johnny Ray. The first part of the video is too.
Johnny Ray isn’t mentioned in the rest of the song, and the song itself isn’t in his style. Kevin Rowland presumably set out to write a song about Johnny Ray then got distracted and ended up writing a completely different song, but left the first verse in because… well why not? It didn’t prevent the song from being a huge hit.
So, I’m wondering; what other well-known songs do something like that?
I’m not talking about songs like I am the Walrus, where all the lyrics are incongruous, nor am I talking about “plot twist” songs where something unexpected happens but it’s still part of the same story. I’m asking about songs where part of the lyrics are about a completely different topic. I’m sure there are other obvious examples but Eileen is the only one springing to my mind right now.
I don’t have any incongruous lyrics to contribute, but I don’t think that you are understanding the first verse of “Come On Eileen.” One of the themes of the song is the recollection of their youth, with references to the music of their parents that they (should) remember so well. The first verse is about their mothers listening to Johnny Ray, not about Johnny Ray himself. Therefore, I don’t think of it as incongruous at all. (Other posters may disagree.)
I don’t know if it will qualify as ‘well known’, but the Grateful Dead sing ‘Looks like rain’.
The song is about a guy facing the first morning alone after a breakup. The first verse is him coming to the realization that it’s happening, and it might be forever. The second verse is about street cats fucking.
Note that Johnny Ray’s career was harmed by his arrests on “moral” charges (he was a homosexual).
The song is about forbidden/secret love. In the case of Eileen and the singer, it concernedyoung love, especially taboo in the Catholic world in which the authors lived.