The best way to say 'You are invited to my party' in Spanish is the following:

-Te invito a mi fiesta
-Esta usted invitado a mi fiesta (very formal way)

If you want to send an invitation card to someone you should write just the word: 'Invitacion'
The vocabulary for the type of celebration is the following:
-Cumpleaños (Birthday Party)
-Boda (Wedding Party)
-Bautizo (Christening Celebration)
-Comunion (Holy Communion Celebration)
-Fiesta de Graduacion (Graduation Party)
-Cena de Navidad (Christmas Party)
-Fiesta de disfraces (Fancy Dress Party)