For a start I would probably refrain from singing the "Fields of Athenry" or "Willie McBride"!!!!
Some songs are really popular and its not so much that they are overused but rather that they are, if you'll excuse the expression, "butchered" by a fair majority of would be singers who have no concept of how they should be delivered nor have a singing voice to match.
There is technically nothing wrong with the songs and if someone sings a good interpretation/arrangement in a tuneful voice it would probably be welcomed.
However at the end of a very busy folk week, when someone number 25 proceeds to give a five minute introduction/background to a song that is very well known by all and then crucify's it by forgetting the words while reading off their well worn crib sheet! This tends to get the "Bloody Hell Not Again" reaction.
I personally don't sing the two songs mentioned above. The first because I sang it about three times a week for three years when I was in a band in Holyhead. and think I've probably exhausted my interpretations library for it! The second because I don't personally like it as it tends to be delivered in a "music to hemorrhage" by maudlin style. But that of course is only my opinion, many others quite like it.
I'm fairly sure that somewhere on the mudcat there will be a previous thread dealing with songs that are considered overdone and hopefully someone who remembers it can blicky it for you.
Good luck with the singing and welcome to an extremely rewarding pastime.