Some more thoughts on test strategy and test plan.
Strategy follows vision. Vision may be viewed as the desired future which is sought to be created or a desired state that is sought to be reached. From a testing perspective, when defining a vision for your test group, it might be easier to articulate the vision in terms of what you envisage your group - to be , to provide , for whom and possibly when. This is not a template but a little aid to help with thinking about your vision.
The vision helps the organization focus on its long term goals and where/what it wants to be. The (test) strategy provides a road-map or approach to achieving these goals. The strategy answers questions such as what do we do to reach our objectives and identifying the means to achieve them. The (test) plan however is tactical in its approach. The plan looks at deploying the means described by the strategy to achieve the desired ends. The plan is mainly about the how of testing and test execution.
At what level does a test strategy reside? It depends. There are test strategies that are defined at an organization level and strategies defined for a specific project or product. The nature of the testing organization, whether centralized or de-centralized will also have some bearing on how strategies are defined. In a centralized structure, the chances of having a common high level strategy is definitely greater when compared to a de-centralized structure where the inclination to have a project or product specific strategy is greater. A test strategy would include items such as the approach to testing, the test design methodologies to use, techniques and tools to use, the levels and types of testing to be performed, reporting requirements, configuration/change management, defect tracking and reporting, etc.
Is the test plan part of the test strategy or vice versa? It depends on whom you ask and what they think these terms mean. There are folks who think a plan derives from a strategy while there are folks who believe that the test strategy is part of a test plan. In some cases the strategy is formulated per feature of a product too. It is important to ensure that everyone involved understands what is implied by these terms and how these tie in with your group's activities and objectives.