Midevil?  How about "Ohhh, oh Oh OH Oh oh oh OH OHH oh Oh oh aahhhhh..."
(My version of a monk's chant)

Medieval songs would likely be in Old French, or Old English - if you can speak either, then sing away.  I've always been interested in Anglo-Saxon.  So I was trying to learn it ages ago - it is quite interesting.  There are many similarities to modern English - and a lot of similarities to modern German.  For example, "bishop" is "biscop", pronounced "bishop."  "Scip" is ship, pronounced "ship."  Complex verb endings compared to English though.  Old Norse is good, and it is very like Icelandic so there are plenty of books on it.

Gaelic is an Indo-European, Latin-based language.  It is spoken in Scotland and Ireland, different languages (not just dialects, as they are mutually unintelligible).  I personally have not tried learning it.  And I have no particular desire to.  It just seems kinda folksy and annoying.  I think that most medieval songs from England, or even Germany, Sweden, Denmark, Norway and Holland, would be in very similar old Germanic languages, not Gaelic (Gaelic would be in what is known as the "late antiquity" - the early dark ages) and in France, Old French would be the norm.  So for medieval songs, Gaelic is certainly not useful.
  I remember watching a history programme - Terry Jone's Medieval Lives (yes, Monty Python Terry Jones - but remember, they were all Oxbridge students)- and in it, he studied the travelling minstrels.  He went to France, and there were a pair of Frenchmen who sang in Old French, and called themselves the Fabulous Troubadors or something similar.  It was odd because they kind of rapped, and instead of "oui" they said "ock", or at least it sounded that way, not sure of the spelling.  So there are people out there who might be able to help you sing in the old languages.

I was visiting my brother today, after his first month at University in Birmingham.  He is doing ancient and medieval history.  He had a good book - the song of Roland - an original Norman song/poem/saga.  It was half in English, half in original Norman dialect - a bit like Germanic French.  If I were looking for Medieval songs, I'd be looking for a version of this.