You have lots of options and most of them can be done without Sharepoint designer  or Visual Studio.

I think the "by the book" approach  is something like this:
Each team has a document  library on their team site
There are several content types and site  fields created  relating to documents  - eg strategies, policies, procedures
Each document library  contains these content types
The teams create  documents in the libraries and fill out the required information about the content type
Then you can use the Content Query Web Part to bring all the similar content together on one page.
However, since you already have all your documents in one place - all I would do is create a site column and content type for those documents which allows people to choose which type of document it is - like the "strategies" meta data. You could then either create a series of custom views and drag them on to different web pages or use the content query web part.

You can read more about content types at:
msdn.microsoft.com/en-us/library/ms472236.aspx
blogs.msdn.com/.../561809.aspx