If delete is not a choice, then you are probably trying to delete events from a calendar that you subscribed to, rather than sync with. Subscribed calendars are usually one way. You have to delete the events from the other end.
Calendars that were subscribed to should show up in a special account called Subscribed Calendars (if memory servers). You'll find them in the same place as email accounts; at the top of Settings > Mail, Contacts, Calendars. It is also possible that some of the calendars you are synced to are read only on your server side as well; that's possible with GMail (and probably MS Exchange) at any rate.
Without knowing more about how you've set up your calendars, what you are syncing with, etc. I can't make any better guesses. Even then, I don't have an Exchange account to play with so I can't give any solid advice on read/write calendar sharing there.