*Cough*
What counts as "irish influenced" anyway? I mean, ask most people what irish music is and they'll either name someone like Daniel O'Donnell and some tweedledeedee fiddle stuff, or bands like Dropkick Murphys and Flogging Molly, most of whom are actually american. As a country, you really might as well say "Here's a thread for all British influenced music" for how well it defines a genre. We've already had Thin Lizzy, and some of the Irish trad stuff on guitar, and trad stuff on violin. Then you have bands like U2, The Chieftans/The Dubliners.
Then there's stuff like this little gem by Stoat, which is unfortunately isn't one of their best songs (the range on youtube is limited), but it gives you an idea of the kind of music they do.
What something a little less odd and a bit more amusing? The illustrious
Dead Cat Bounce are one of the best bands in the comedic business, if you ask me:
I guess what I'm trying to say is, if you're looking for music that is influence by Irish
Traditional Music, then that's great, it is a genre with a great culture and background, but please make the distinction. It's a little insulting to Irish musicians to assume that that's all the entire country has to offer