You and your family need to always be ready for tornadoes. Know what to do. They can strike any time of the year. Just a few months ago in late November an EF-2 tornado tore through Lake Tenkiller, destroying the marina, buildings and homes. On average, April, May and June are the peak months. While late afternoon and early evening are the most common time, they can hit at any time of the day or night. Oklahoma averages 56.