The song is obviously not up to today's ideas of child education. The tune certainly has a "hook", but most of the arrangements mentioned above are even more corny than the lyrics. "Bossa nova" – haha!

What intrigues me though is the title/chorus. Katzenelnbogen is a village in SW Germany of then 1500 inhabitants, hardly known in the USA. But in the Middle Ages it was the home and eponym of influential counts and, to the point here, famous rabbis. Wikipedia tells us that the authors Al Hoffman and Dick Manning were of Yiddish mother tongue (born in the tsar's empire), thus are likely to have remembered the rabbis' name rather than the village's – though the latter would seem most adequate to the "message" of the song.

Therefore, Ossenfeffer ought to be Yiddish as well. "Feffer" is easily identified as pepper, but to read "Ossen" as oxen/Ochsen may well be a mistaken projection from the Dutch and Low German word. Anyway, ossenfeffer seems to be a dish of the Yiddish cuisine.

Gilly is a short form for the name Gilead, popular with Jews worldwide.

To sum up, the story may originally be set not in wirtschaftswunder Germany, but in a Russian shtetl, mostly imaginary.