I loathe the Fields of Athenry, apart from the sad adoption by Celtic fans, it's a maudlin song, and Pete St John has written many many better songs.
I fell in love with The Band Played Waltzing Matilda when I first heard it sung at Chichester Folk club, by a lovely lady called Georgina. Then it seemed that everybody was singing it, so I gave up doing it. Now I am singing it again, as it's not so ubiquitous now. I still struggle to get through the lines, "The armless the legless, the blind the insane", they give me a lump in my throat that's hard to sing around.