Single term for "elephants going berserk"
Solution 1:
The elephants rampaged (M-W: Rampage: to act or move in a wild and usually destructive way).
Musth as above is great, but only applies to males, and corresponds to a particular (sexual) context.
Solution 2:
Perhaps musth is the word you are looking for:-
An annual period of heightened aggressiveness and sexual activity in male elephants, during which violent frenzies occur.
One would say, "the elephant was in musth".