They are all very close in meaning but there is a slight difference.
Approach, method and way can refer to how you set about/ start a certain task. The manner in which something is done.
Way and method can also refer more to an actual fixed procedure, often according to a definite established, logical or systematic plan. 'There are three methods/ ways to cook an egg.'
Means often refers more to what you use. The medium or instrument used to obtain a result.