How do I change the email address used by Calendar to send invitations?
Standard way:

Go into Mail preference with

Mail > Preferences > Composing

and then change the following option: “Send new messages from”

If this did not work:

Go into Contacts and create a new card or pick the one with the mail address you want to use (i.e. your work e-mail).

Afterwards, go to the Card menu and select “Make this My Card”.
This mail address should now be your default for Calendar.