We hereby invite you to the party. But this is exceedingly formal. Hereby is a very official word you'd see in things like legal documents. Just say "We invite you to our party".
Invite is an informal way of saying invitation.
invite - definition. American English definition of invite by Macmillan Dictionary
It's also used online to refer to invitations to various sites, communities, etc. In this context you use invite but not invitation.