"Us" pronounced as [əz ~ əs] is common in Britain as an equivalent of "me" but only in an unstressed context. If it were a question of who you were giving a kiss to, the answer would be "me" [mɪi]. For this reason, it's unlikely to cause any confusion. It also, though, is why it can be common in even less informal situations. It can be quite difficult to change to using "me" in all situations without feeling that you're sounding over-emphatic.
In American English, you wouldn't see "us" standing in for "me" in any of these cases. You might hear something like palindrome's example "Come on, give us a break!" but it would mean that someone speaking for a group is addressing someone. For example, you are with your friends at a bar; one friend is telling a lie to the group and another replies "give us a break!"
I wouldn't even say that it was "very" informal. In BrE it's just informal, but very common. In fact, I would almost say that those who never use it are people who are consistently formal in their speech regardless of the circumstances. There aren't many of those around these days.