You, me and your father ________ going to party. (Are,am,is)?

It's "You, I, and your father are ..." Plural subject requires plural verb, and subject requires "I", not "me".

Now learn the dative case. Suppose I say "Give me your book." The word 'me' is in the dative case because what I mean is "Give TO me ..." Any time you have to, by, for, from, and so on, that is dative case.