When I got my iPhone 5, the Add Event button in Calendar was greyed out. I have tried adding events using Siri, and that doesn't work either. Why not?
IPhone – I can’t add events in the calendar
iphone
Related Solutions
Tapping on an event should give you an edit button in the upper right. From there you scroll down to the very bottom and will see the option to delete the event(s).
delete event > 
Go to Settings and click iCloud and turn on Calendars.
If that doesn't work, while in your Calendar, look at the bottom - "Today," "Calendar," and "Inbox." Click on Calendars. Somehow my "Home" calendar (which is where I save most entries, as opposed to "Calendar" or "Work") was unchecked. I couldn't see any old or future entries, and when I added entries and hit save, the day would be empty. When I re-checked "Home," everything reappeared.
It just wasn't showing "Home" entries. I hope your problem is this simple because I know how you feel like you're losing your mind when something like that happens!
Best Answer
I found it to be my password for iCloud. It dropped out after the update. I entered it back in and verified it and the calender came back online. Stupid update errors! enough to drive you bonkers!