Interesting comment on the abhaile (homewards) as an explanation for weela weela awaala. One other item that would suggest this version as distinctly Irish is my understanding of the river Saile as being the Irish for the Willow river, saile meaning willow tree, as in The Sally Gap in the mountains above Dublin (rather than the dirty river as suggested at the start with its shorter vowel and harsh ending, although it too is possible) . Always called, by true Dubliners, as Sally's Gap (maybe she owned the unfortunate horse) it is the Willow tree gap. Although for a long time as a kid I heard it and sang it as the river sai'ed in the Dublin accent for side, where single vowel words tend to have the vowel lenghtened and pronounced twice; words like wo'ords, or "come hee'ar", for come here or "whe'ar" for where but I think Saile is the correct word since as kids we would have heard it long before we read the words.