I have the same problem; and I know nothing about MS Office beyond how to install it.
My client has about 10 users with a combination of Office 2007 and Office 2010.
They asked me to add an email address to one of the machines (running Office 2010) and then decided that they did not want to use the new email address anyway. Prior to adding the account, there was no issue with calendar invitations. Since then, when this machine sends an invitation it is received as an email by the recipient. This machine correctly receives invitations though.