Havoc means widespread destruction. Wreak, a mostly archaic verb, means to bring about. So to wreak havoc is to bring about widespread destruction. Havoc may reek, and it may cause a wreck, but reek havoc and wreck havoc make no sense.
Examples
The misspelled versions appear often—for example:
The combination of reduced sunlight exposure, physical activity and socialization can reek havoc on a person’s psyche, Matlock said. [The Decatur Daily]
Although the Panthers and Buccaneers are both 4-8, a division rivalry can wreck havoc on a team’s playoff chances. [Atlanta Journal Constitution]
And these writers use wreak havoc correctly:
Holiday blizzards wreak havoc in central United States. [BBC]
Winter can make you go into hibernation mode and crave fatty foods, which can wreak havoc on your skin. [The Utah Statesman]
The past tense of wreak is wrought. But because this irregular conjugation is quite rare, getting it wrong is understandable. This writer uses the correct form:
Meanwhile, the Great Depression wrought havoc with anticipated real-estate gains. [Seattle Times]
