The purpose of testing is to find defects, not to pass easy tests. A test strategy basically tells you which types of testing seem best to do, the order in which to perform them, the proposed sequence of execution, and the optimum amount of effort to put into each test objective to make your testing most effective. A test strategy is based on the prioritized requirements and any other available information about what is important to the customers.
Because you will always face time and resource constraints, a test strategy faces up to this reality and tells you how to make the best use of whatever resources you do have to locate most of the worst defects.
Without a test strategy, you are apt to waste your time on less fruitful testing and miss using some of your most powerful testing options. You should create the test strategy at about the middle of the design phase as soon as the requirements have settled down.