Strawberries can be eaten without washing first but in my opinion it's always best to wash Strawberries before eating them especially if the strawberries came from a store or somewhere else that you're unsure of whether pesticides were used.
Washing the Strawberries will remove pesticides as well as any other bacteria that may be on the Strawberries.
I always wash all Strawberries and any other fruit before I eat them just to get rid of pesticides and other bacteria that may be on them.