I don't know the best way to say "tea party", either. More specifically, what the best way to say "tea birthday party" or something like that would be. The dictionary says "teselskab" but that sounds more like the Boston variety to me.
So if you could help with my grammar that would be great. I'll probably change the wording around a bit in the final version so it doesn't sound so contrived.
I inviteres til min _____(te)_____ fødselsdagsfest!
Kom se min nye lille lejlighed og spis te-sandwich og muffins og drik te (eller andre drikkevarer). Det bliver hyggeligt!
(ingen gaver, tak)