Outlive, outlast, survive are comparable when they mean to remain in existence longer than another person or thing or after a given experience.
Outlive carries a strong implication of a capacity for endurance and is especially appropriate when competition, struggle, or the surmounting of a difficulty is also connoted.
Outlast differs little from outlive but usually stresses greater length of duration rather than greater capacity for endurance and therefore may be employed when comparison is more important than a suggestion of superiority or when the fact of existing longer is more important than the length of time involved.
Survive may be used as an intransitive as well as a transitive verb; in general it suggests merely a living or existing longer than another person or thing, or after some event (sometimes implied rather than expressed) which might bring about his or its end.