Remember fish don't just live in the sea, and there are rivers and lakes all over Ireland. The best fish I ever had was poached salmon trout from Lough Neagh. I'm not too sure how it was cooked, just fried I think.
There are always Irish mussels in the supermarket here, so I imagine they get exported to other places as well.
As for corned beef and cabbage, I've heard of that, but it's just a substitute for the real thing, boiled bacon and cabbage.
I imagine there are a lot of fish recipes from Newfoundland, and that counts as more Irish than anything - I've a recipe and poetry book from there somewhere, and it's got about a dozen different recipes for Colcannon, and about as many ways of spelling it.