Strawberries are not berries actually, but yes bananas are

By technical definition, a berry is a fleshy fruit produced from a single seed. The strawberry, however has its dry, yellow “seeds” on the outside (each of which is actually considered a separate fruit). True berries, like blueberries and cranberries have seeds inside. However, the banana fruit is a berry for the same reason strawberries are not.

There is a theory that strawberries were named by 19th century children who picked the fruit, strung them on grass straws, and sold them as “Straws of berries”.

http://factsram.blogspot.in/2012/12/tips-to-weight-gain-naturally.html