In Ohio - I ususally don't plant peppers, tomatoes, cucumbers & other warm weather veg till around Mother's Day (mid May), but my dad always said Memorial Day weekend is when you plant. But I have had no issues with loosing my plants after Mother's Day. I just always make sure I am prepaired to cover them w/ a blanket if there is a change of frost.
As for the strawberries, mine that I planted a few years ago are up & thriving despite a few frost & snow about 2 1/2 weeks ago. But I'm not sure if that is because they are already established... call a local greenhouse/gardening store & double check. Or if you want to plant them - just make sure you watch the weather & cover them w/ a blanket or sheet at night to protect them from frost. But next year when they are established - they should be fine.
The cold weather plants (broccoli, sprouts, potatoes, onion, lettus, ect) are safe to put in now & actually they sometimes perfure to be planted now & don't need the protection from frost, just hard freezes.
Good luck on the garden - they can be fun & educational even for kids. Plus, there is nothing better then eating something you grew (and canned) yourself!