Ceuta was originally taken by the Portuguese in 1415, at the same time that the Portuguese started a strong programme of exploration that includes conquest and/or settlement of the Canaries and the Azores.

The crown of Portugal was united with the crowns of today's Spain -- namely Castile, Aragon and Navarre -- when a young king Sebastian of Portugal died heirless in 1578. His regent Cardinal Henry died soon after, and Philip II of Spain moved to claim the crown of Portugal for himself as he was also a descendant of the royal family of Portugal.

When Portugal re-gained its independence decades later, Ceuta remained a possession of Spain.

Melilla was captured by Spain in 1497, as the reconquesta/crusade moved past Granada at the southern tip of continental Spain onto north Africa and the Mediterranean theater. The objective was rather defensive, namely to secure that region against possible counter-attack. Over time, conflict in the Mediterranean grew and so did investment in Melilla.

why the Strait of Gibraltar is British.

The strait isn't British, it's part of the ocean. The Rock of Gibraltar as well as a town of the same name at its base is British. It's that way because an Anglo-Dutch force captured the Rock and its harbor from the Spanish in 1704, during the War of the Spanish Succession, and the territory was ceded to Britain "in perpetuity" in the 1713 Treaty of Utrecht. It has been a major Royal Navy fleet base in the past, and although Spain presses territorial claims on Gibraltar, referendums in Gib on joint sovereignty have failed miserably -- in 2002, 98.48% of the population voted against joint sovereignty with Spain.

Edit: I a word