Firstly, decide who is your audience, i.e. who are you writing the strategy for? What will they use it for? That should then determine what level it should be written at.
A very effective idea I saw recently was to write the strategy using MS Powerpoint, not to give as a presentation, but as a document. Use standard Powerpoint font. What this did was force the thinking into getting the points across with minimum words, maximum impact - just as you would have to do in a presentation. It really worked well. It is true that the level of detail is not there, but you could argue that providing that everyone understands the terminology and the concepts, the detail is of less importance. If the understanding of terminology and concepts is not there, then you probably have a bigger problem than getting a strategy across.