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Raspberries (and blackberries and all those similar) have a short shelf life which is why you rarely see them sold in stores. They might last a day or two but go bad fast (even with refrigeration.) Blueberries also go bad quickly but can last a bit longer. Yes, refrigerate them, but don't wait too long to eat.
Answer: Your strawberries should be fine. You can safely store fresh, whole strawberries at room temperature, says the U.S. Department of Agriculture. That said, you should always try to refrigerate your strawberry purchases as soon as you get home from the store.