When we were kids in Tottenham (you can guess how long ago)we used to sing "We won the cup /we won the cup ee i addio we won the cup" .The iaddio bit i thought was nonsense until I went to Ireland about ten years ago and heard my friend's young daughter sing to the same tune   " ta mamas isteach ta mamas isteach duirt daddio ta mamas isteach " In the Irish (which I'm sure I haven't reproduced properly here) it sounds very similar.The words mean something like Mummy's at home tell daddy that mummy's at home.
The Clancy Bros used to sing a song THe Juice of the Barley with a chorus that I always assumed was nonsense "Bunya na bo is na Gowny and the Juice of the Barley for me" which isn't nonsense atall.It translates as The milk of cows is for calves and the juice of the barley's for me.
Brendan Behan wrote that the words of Lillibulero which was sang by the apprentice boys at the siege of Derry and which wqs widely perceived as being nonsense meant The Lilly (the emblem of the boys who were all Gaelic speakers) won the day.
There are a load of other examples but I can't think of any at the moment