Various expressions are possible. None of them is as florid as your Japanese one. (But then, who would dare to compete with Japanese when it comes to floridness).
"Kreischen" (mentioned first above by RoyPJ) is probably the most common word used for that phenomenon, although the word is void of poesy; it is rather matter-of-fact-ish.
I list a number of possible sentences that come to my mind:
Als der Star auf die Bühne sprang, fingen die Mädchen an zu kreischen.
Als der Star die Gitarre ergriff, wurden die weiblichen Teenager hysterisch.
Als der Star zu singen began, fielen die Backfische in Ekstase.
Die Mädchen gerieten in Verzückung.
Die Mädchen schrien wie am Spieß.
The only one here, so far, with a certain graphic quality is "schreien wie am Spieß", although this is not a particulary good match as initially it means screaming of deadly pain and terror, not of joy. Anyhow, the sound would be similar. Perhaps one could enrich it by combining:
Die Teenie-Mädchen gerieten in Verzückung und schrien wie am Spieß.
Speaking of acoustics, I see one more way to express this (based on the experience of time spent on my uncle's farm when I was a teenager myself): Als sich der Star das Hemd vom Leibe riß, erhob sich aus den Kehlen der Groupies ein Geschrei wie zur Futterzeit im Schweinestall. But note that this is nothing I have ever heard being said, nor does it seem appropriate for use in any normal context. I made it up ad hoc based on the acoustic similarity. Town-dwellers would not understand the analogy, I suppose, but villagers will.