One of the issues with finding information on child-centered folk songs like 'Magalena Hagalena' (which in variants gets called things like 'Catalina Magdalena' or 'Katharina Hagalena' - you can see some other variants in comments at a folk internet forum here) is that nobody thinks that it's important at the time, so nobody writes very much down about the song - you often can only find out things about its like in off-hand references in other contexts. And searching for it on the web in archives can certainly be a hassle, because there's lots of variants of the tune and people spell things differently.

Luckily, there is actually an academic paper on this tune by one Fredericka Schmadel on her academia.edu page which...will have to to do (Schmadel is more interested in how the tune is used within camps for girls in Indiana than its precise origin). Schmadel believes that the tune comes from a white English-speaking American background, likely in the 1940s and 1950s, related to camps for girls (it seems less common, though not unknown, according to Schmadel, in the boy scout movement).

The name of the person (or giant or witch?) that the song is about is is meant to be deliberately fun nonsense, and the sources of the first half of the fun nonsense seem to be vaguely Spanish-sounding names like 'Magdalena' that often share an assonance and a rhythm - a-UH-i-UH! These are followed by words which sound Hawaiian to American English-speaking ears - note the two syllable form of all the parts of her name after 'Magaleena', all of which end with a vowel rather than a consonant, for example - 'Waka Taka'; Schmadel makes a comparison between the nonsense syllables here and the nonsense syllables in David Seville's 1959 hit 'Witch Doctor', which features sped up vocals on the chorus singing nonsense syllables (and which is clearly a precursor to The Chipmunks).

Other versions of the nonsense chorus try to make sense of the nonsense by turning them into more like real names: "Catalina Magdalena Hoopensteiner Wallendiner Hogan Logan Bogan" but I agree with Schmadel that these sound like later rationalisations. A while back on /r/AskHistorians I tried to track down the origin of another old campfire song, and it seemed reasonably likely to me that the song was a mutated version of a novelty song from the 1940s, or perhaps a degeneration of a mosquito spray jingle from the 1930s. It might be that there is an origin to 'Magalena Hagalena' along these lines which is lost in the mists of time; alternatively, it could have been made up by a 8 year old girl who was good at being funny in 1943. But that's the nature of folk music - knowing the origin is sort of beside the point, because the point is not where it comes from but how it's used now. And here, Schmadel argues, the learning of the song is a sort of ritual 'bringing the group together' thing which serves to delineate an in-group (e.g., the girls at the camp) in comparison to an out-group (e.g., Magalena).