This page will give you links to a number of sources for Irish traditional music on the internet. There are many more out there, but hopefully between then you'll be able to find words and/or music to most songs that you could want.
Rick's Airs, Anthems, Ballads, Canons, Ditties, Folksongs, Hymns and War Songs. This is our favourite archive although surprisingly enough it is based in Germany. Alternatively there are archive from several European countries.
The largest database of old songs is actually English and published by Oxford University. Search 30,000 archived ballads in the Bodley Database
Another very good resource is this Irish site which will play many of the tunes as well, although there are only a few songs.
And Zaphod's Site has another
325 songs.
Finally, another new traditional site (if that's possible) - Richard Moon' tune database