If every action gives an equal and oppositte reaction,according to the third law of motion, how does an object move?

Action and Reaction act on different objects. So there is no question of their mutual cancellation.

Object move because of various forces acting on them

Object moves because of various mass. If a 5kg mass excert a force so that a 2 kg mass gain 2m/s velocity then the work done by first body is 4j and thus the expression of velocity of first body is

                       1/2×5×v²=4  => v=√(8/5)