Some of these I haven't thought of in years... "Sunrise, Sunset" from Fiddler on the Roof, "You'll Never Walk Alone" from Carousel. I used to sing both of these in a choir, and I'm sooo thankful I wasn't singing solo. However, I did do "You'll Never..." as an audition piece, and I found listening to the tone of my own voice, rather than the words, helped. They stopped me early, so I guess it got to them too!
My best advice would be to not let it worry you if the song gets to you. If you show some emotion, your audience will respond sympathetically. (I always feel very sorry for the bugle player who has to play at war memorial services.)
I heard "First Christmas Away From Home" for the first time last July, and I *bawled*! Now it's the holidays, I have a recording of it, and I don't think I can listen to it!
Waaahhh!! But nice to know I'm not alone. CIndy Ellen