"Всегда" means "always". "Навсегда" means "forever", that is "always from a given point in time". "Вовеки" is a high style alternative for "навсегда". It literary means "for all remaining ages" (во веки) or "for full remaining lifetime". "Вечно" means "eternally" in the standard language. It is used to describe a very long period of time and is stronger then "всегда". I mean it can be used to emphasize the eternity: "потомки будут вечно помнить подвиг героев". In informal speech it can be also used instead of "всегда": "ты вечно опаздываешь".