I often hear when people say something like "He left Jack and I a message", or "They sent an invitaion to Sarah and I to attend...".
To me, it seems like I is not the right word here. I would say me, but people say I so often that I start questioning myself. Who is right? Is it corrct way to say that? Is it colloquial English, or, perhaps, American English? Why people say I, not me? Is it only myself who gets convulsions when hearing that?

Can someone clarify, please?
Thanks,
PLeXuZ