I was looking on line for an answer to the same question, and didn't find it...but I figured out how to do it and thought I would share -- better late than never. Close Outlook, To open, double click on the icon while holding down the shift button. Upon opening, the outbox appears at the bottom on the folders column. Click on it and you can see it's contents.
To sync your email account between Outlook and your device, you can add the account in both Outlook and in the device. You do not have to turn on Sync Services in Outlook. It might take some moments for your Outlook data to appear on your iPhone, iPad, or iPod.
I don't know how long it continues to appear there. I clicked on it quickly, deleted the stuck items and once those were gone and the other items sent, the Outbox disappeared again.
Hope that helps you or someone else looking for this answer. Have a good one!