Approach has more than one meaning. If I move towards you, then I am approaching you. However, approach can also be used as a noun. One of its uses as a noun is a synonym for 'method.' "The experts outlined a fascinating new approach to this problem" = "The experts detailed a fascinating new method for dealing with this problem." A strategy is a bit grander than a mere 'method.' It suggests a general approach to a wide area of policy or study. "Obama's strategy in Syria has never been clear."