Depends as always ;-)

"Whom did he hit with the gun?" - "My father, my sister and me."

"Who was at the party?" - "My father, my sister and I."

depends-
the man spoke to my father, my sister and me

OR
My father, my sister and I went/came/saw etc

depends-
the man spoke to my father, my sister and me

OR
My father, my sister and I went/came/saw etc

when unsure simply take the other people out of the equation, e.g.:

the man spoke to me - you can't say: the man spoke to I
I went/came/saw etc - you can't say: mewent/came/saw etc

We have a disjunctive pronoun here (because of the "and") which means that informally at least you can always use "me". No one would ever say "I" if this phrase was in a stand-alone context. (cf. French ... et moi)

In formal contexts, and especially where the next word is a verb of which the "I" is part of the subject, better to use "I".

My parents, my sister and me live in

Does anyone remember the lokal in Schwabing "Meine Schwester und Ich"

In BE more that AE one tends to use the "me", even when it is not correct.

Gast, in Deinem Beispiel Nr. 4 wäre es m.E. immer und nur "sister and I live in ..."

ok seriously - please see: http://www.askoxford.com/betterwriting/classi...
and/or
http://www.askoxford.com/asktheexperts/faq/ab...
formal or informal - correct is correct and incorrect is incorrect

My parents, my sister and me live in...
sounds like one's mother and father were first brother and sister