A test strategy in my definition includes a test plan, types of tests to be performed, procedures to perform the tests, tools needed to perform the tests, and imput test datasets needed to perform the tests. All rolled together is your strategy and approach to testing the product.
OK I'd say you also need:
- roles & responsibilities for each member of the team
- entry/exit criteria for each stage of testing
- Schedule (when you will do what tasks)
- The different stages/types of tesing you will perform
Together with icruiser's post these are just a few items that you might want to consider when you are drafting a strategy.
In a small team I would say the Test Manager should write the strategy. In a large(r) team you might have many products which each require strategies, so it would be more appropriate for Test Engineers to create the strategy and agree an approach with the Test Manager.
Really though I suppose the most important thing is to find an aproach that is suitable for your firm that you and the rest of the test team are comfortable working with.
The test Manager or Engineer can do the strategy, depending on who is running the project. When I Managed a QA group, if I was running a new project I did the planning, if I had appointed a lead for the project, I had them do the planning, of course I helped out when needed to make sure they were on the right track.