(べんきょう) To study. 勉強 is used about learning a whole subject, like philosophy or French or, say, Japanese. In other words, it is a process which takes months or years. Unlike 学ぶ, 勉強 is something you can do on your own.   $$$
(まなぶ) Two meanings: to learn something from a teacher. Also, to learn one random fact (not a whole subject). 学ぶ can also be used like, “I learned xxx in college.” Also, 学ぶ means that you have learned it, while 勉強 means you are studying it, but don’t necessarily know it yet.
(ならう) To study a subject. More casual than 勉強; you can use 習う about a subject that only takes a few months to learn. Like 学ぶ, generally there is a teacher involved.  It’s used for subjects where there are routines to be memorized and performed, like English, dance, karate, flower-arranging. It’s not used for math, science, or religion.
(じしゅう) Self-study.