Click around on some of your IMAP folders. The inbox for Gmail works for me.
At some point you will get the option in the main menus to...
Edit->Purge->Purge Options->Folder Tab
There you can set where sent mail is copied.
Now don't ask me about fixing duplicate sent items, since Outlook will save
one, Google will save one if you've set it that way (yours too, perhaps, if
you use something else), and once they sync, you'll have 2 of everything
you've sent through the IMAP account..
Too bad I have POP accounts too and want the ability to use IMAP to see sent
items through the Web interface too.
Btw, I'm using Outlook 2007. Welcome to the mess.