Oh, it's difficult to explain, it's often just the compatibility with other words matters, like where to say "many" where "a lot of" in English.
использовать - virtually to use a machine, a method, an object for some purpose
пользоваться - has more polite implementation as for things being given to use
воспользоваться - use the opportunity
употреблять is similar to потреблять - to consume, but употреблять implies some utility, avail
применять - apply