How do I send a calendar event from the iphone calendar via an email or imessage?
The simplest method would be to use a contact in your address-book and add them as an invitee to the calendar event.

You will be prompted to send an invite to them.

EDIT: Previous link sucked.

Here are the steps circa iOS 9:


Launch the Calendar app on your iPhone or iPad
Either create a new event or tap an existing event that you'd like to share
Tap on the Edit button in the upper right hand corner
Tap Invitees. Add all the email addresses of the people you'd like to share the event with


EDIT 2: Added iOS 11 details.

Here are the steps circa iOS 11:


Launch the Calendar app on your iPhone or iPad
Either create a new event or tap and existing event that you'd like to share
Tap "Invitees"
Tap "Add invitees"
Either enter an email address, or tap the (+) at the right to select from your address book