Green’s Dictionary of Slang

1. something or someone seen as very funny.

1919		Wodehouse Damsel in Distress (1961) 209: You’re a shriek, dadda!
1925		Dos Passos Manhattan Transfer 132: Oh, Jimmy you’re a shriek.

2. something ostentatiously fashionable.

1914

Bulletin (Sydney) 16 July 10/4: Last week Elvira Jibkat, young and pure, and oh! so fair, / Was hacking at a Raphael with a knife / (She wore, I need not say, the latest shrieks in clothes and hair); / Men rushed her. She became involved in strife.

3. an excl. of alarm, annoyance or similar emotion.

1900

Bulletin (Sydney) 15 Sept. 7/3: The Bulletin culls the following printed shriek from a huge two-column advertisement, published in Sydney, of the Canadian Independent Order of Foresters – that curious cheap-Jack life assurance device which recently struck this defenceless country.