I've had the same Paddy's gig, in the same venue, for the same landlord for 10 years running and we basically stick songs in the set from anyone with even a slight Irish link...
As well as diddly-diddly favourites like Dirty Old Town, Lord of the dance and Mursheen Durkin, we do stuff by Saw Doctors, Van Morrison, Boomtown Rats, Thin Lizzy, U2 and The Pogues. We've also been known to slot in some Bobby O'Marley!!!
Wear something green, say "to be sure" a lot and have fun!!