My understanding is this simply isn't possible. Google creates a folder in Outlook for every label. If you assign multiple labels to a message, Outlook downloads multiple copies of that message, one for each folder. And of course, within Outlook, you can only put an item inside a single folder.

This goes straight to the heart of how Outlook and Gmail were designed to operate. Outlook is built on a folder hierarchy, while Gmail is a completely flat structure. They've tried to bridge the gap somewhat (with the labels-folders equivalency), but it's a bit awkward. The long and short of it is you cannot, within Outlook, take Outlook's entire paradigm and replace it with Gmail's.