Whether the Strawberry is a fruit or not depend on the definition used.
Botanically, a strawberry is not really a berry or a fruit, the result of a fertilized plant ovum. A strawberry is actually an aggregate fruit containing the real fruit, the strawberry seed (called Achenes). The strawberry is an enlarged vessel, not reproductive material, with seeds on the outside skin rather than having an outer skin around the seed like most berries.
Gardening and Culinary
Gardeners and cooks consider the strawberry a fruit because strawberries can be grown in the garden, in containers; indoors or outdoors and according to Williams and Fisher (1917, pg 227) because strawberries are seed-vessel eaten with sugar or as a dessert. Choose the definition you like best, for my money they are an invaluable part of any garden or meal for that matter.