For any online music I always look to YouTube because it's not illegal downloading and you can still listen to a lot of great songs. For a rocky/celtic sound try listening to Flogging Molly (one of my personal favorites) or Haggis. Not that they are "irish music" but they definately have a celtic sound to them. Enjoy!

http://www.youtube.com/watch?v=KPYLxF6Jgc0
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Hi, We listen to streaming radio over the web called - live365 - radio stations of all genres. We've been listening to Irish music all weekend this way.

Pick the radio station that best fits your musical tastes and listen all day...they have many Irish music stations to chose from.

Have fun.
Source(s):
http://www.live365.com/index.live

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Another live streaming Irish Music website is Last.fm, a music site I found through answers here on Mahalo and feel I should pay it forward to you, flawless selection of music and if you just click the radio button you'll get streaming irish music for as long as you wish.

http://www.flickr.com/photos/33749589@N07/3368920735/
Source(s):
http://www.last.fm/music/Irish+music

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Go to Pandora.com and create an station. If you have a favorite artist or Irish song, you can start with that and then Pandora takes over with similar music in that style. I like it because it helps you branch out to other artists that you may have not have thought of.
Source(s):
Pandora.com

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