a loud discordant noise.
a hangover.
a state of depression or bewilderment.

In a sentence:
After a heavy night of drinking, Carl liked to wake up the next day and proclaim, “I have a hell of a katzenjammer,” to impress his frat brothers and escape reality one more time.

In a different sentence:
Seeing his cousin in the shower, Julian was so surprised that he was forced to emit a horrified katzenjammer, and then start drinking—which led to another katzenjammer—and then start going to a psychiatrist (plagued, as he was, by yet another type of katzenjammer).

Fact:
During World War I, American resistance against all things German led to a name change in the comics section of The New York World, as “The Katzenjammer Kids” became “The Captain and the Kids.”