The "Musha ring un do um a da" and the "Whack fol ma daddy-o (or laddie-o)" WERE originally Gaelic, they are just a phonetic pronunciation of the original Gaelic.
Now here's where you have to take it on faith; I KNOW that they are both originally Gaelic because I've seen the traditional lyrics both in a friends book of Celtic music AND on a folk song web site a couple years ago.
My memory is fuzzy but I think Declan had the first part right with "Bainne na mBó ins na gamhna" because I remember the original Gaelic looking absolutely nothing like the song sounds.
Unfortunately I don't remember the name of the web site I saw it on, so I might as well be telling you that I saw Bigfoot. I think I followed the link from a RenFest performers web site. If I can find it again I will post the link on here.

Cheers,
Brian