First, you need to download and install Microsoft Office HTML Filter. Then open your document in Word, go to File menu, select "Export To" and select "Compact HTML". Using Office HTML Filter, click Add button and add the HTML document saved, then click Apply button. Just beware that the stripping this way produces strange results on more complicated documents and you'll still have to go through with an HTML Editor to get it correctly done.
Now that that answers your question directly, I would do it Fengall's way. Actually, I do it by saving my document in html form, opening it in my HTML Editor, highlighing all the office stuff, using Delete key a lot, then the Remove/Replace function in the editor to clean out a lot of the other inline styling for tags I don't want. Then I customize page the way I want, validate it and I'm done. Probably a longer way my way, but I love this stuff so don't mind.