I was born and raised in Oklahoma, always lived around the vicinity of Tulsa for 74 years. Tornadoes can occur anytime of the year and seem to be occuring with more frequency in many states. As others have stated it's a good idea to have a weather radio that will broadcast an alert, know what county you are in and what towns are close by. Also be aware of any Park or local storm shelters. Remember there are far more days without tornadoes than with them. There is less chance of severe weather in July and August but the heat and humidity can be uncomfortable. Late September and October are more pleasant. Our favorite state park is Broken How but it can be crowded. For a quiet park but a little isolated try Osage Hills state park