Havoc means widespread destruction. Wreak, a rare verb most common in British English, 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 are nonsensical phrases.
The past tense of wreak is wreaked, so the past tense of wreak havoc is wreaked havoc. Forget the old, oft-repeated myth that the past tense of wreak is wrought. Wrought is an archaic past-tense form of work, and it serves as an adjective in its own right, but it has nothing to do with wreaking.
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]
Tropical Storm Isaac has wreaked havoc on the GOP convention schedule and is expected to take aim for the Gulf coast. [Wall Street Journal]
The move comes two months after a software update wreaked havoc with payments processing for 17m accounts. [Financial Times]