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Say If I'm running to north at a very high speed. And as I'm running, I'm shooting a beam of light toward west, will the light go completely west, or it will have some degree toward north too?

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You may be suffering from some difficulties of vocabulary here. Running imposes no forces--in the meaning that physicists adopt--on the light at all, though it does mean that your frame of reference differs from that of a person standing still. – dmckee Oct 1 '12 at 2:52

First, for clarity your scenario doesn't involve "forces", as the term is used in physics.

But to answer your question, from the perspective of someone standing still, they will see the light move in some direction between North and West (That is, they will see the light moving somewhat towards the north, depending on how fast the runner was running).

From the perspective of the runner, he will see the light move directly towards the West.

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