Is there any way to force Visual Studio to copy selected code to the clipboard as unformatted text?
When I am copy-pasting code into Word or more often Outlook
The Visual Studio Extension Copy for review may be handy for you. Actually, it does not do unformatted copying, but applies it's own simple text-based template.
It supports a "Stack Overflow" format, which just removes the leading whitespace, while keeping the indentation as much as possible, and introduces some sort of header.
Get it from the from the Visual Studio Gallery and try it out.
Disclosure: I am the author of that Extension. Please notfiy me, if I can improve it to your needs.