I have been struggling with this for days. A colossal waste of time I might add! Here are a few tips:
Outlook can sync to any one of multiple calendars in your ios device. Make sure you are viewing all your calendars on your device, because it may be syncing correctly but you may not be viewing the correct calendar. Also, in settings, make sure that your default calendar matches the one you are syncing with.
In itunes, go to Edit -> Preferences -> Devices and Reset Sync History. Also in itunes on the info tab of your ios device, scroll down to "Advanced" and check "Replace information on this iPhone"
Finally, in Outlook you can have multiple calendars, but itunes will sync with the default calendar.. One big problem I had was that I was using multiple account profiles, and I was syncing with the wrong profile.
I am still having one big problem. While notes and contacts work fine, and the calendar copies nicely from Outlook to the iPhone, I cannot get calendar changes on the iPhone to copy to Outlook. If anyone can help me out here I'd be very grateful! I suspect that it is a problem with Outlook 2013.