Strawberry plants can be propagated asexually by allowing plantlets on the ends of stolons ("runners") to grow in soil.
But the actual strawberries are the result of sexual reproduction, as they grow from flowers.
Surprisingly, the red parts which are eaten are not really fruits at all - they are in fact called false fruits. Nor are the "pips" on the outside simply seeds. The pips are in fact fruits called achenes, and they are embedded in tissue which is derived from the receptacle (end of the flower stalk).
And no - from a botanical point of view they are not berries!