while I haven't been to Mulligans, since you asked about Irish food, you could try St. Stephen's Green in Spring Lake Heights (Rt. 71, the site of the old Eggiman's Tavern) which I find really fairly decent... you also can't go wrong with Harrigan's Pub or Rod's in Sea Girt....
I haven't been to Mulligans in a long time, but I remember it being okay for pub fare. Things may have changed, but the dinner menu was nothing to write home about.
They get a mixture of locals and golfers ( in season ) from near by courses ..The bar food is ok and will not kill you .. Stay away from the dinners .It is a BIG drinking crowd who will eat to stay alive and have the ablity to drive home ..