This is a very odd idiom that is not used very much. The best way to rephrase is that "you were caught". You would use it if someone did something wrong and were caught doing it, but after the fact. The "bang to rights" is similar to "caught red-handed" (i.e. you actually did do it), but less judgmental (i.e. the person who says it is not angry or upset and isn't going to do anything about it). I have not seen the movie, but he may have used "us" to describe both himself and Gromit (us = Wallace AND Gromit), but you are correct in that either works.

First, the expression is said in an odd way. When someone is being emphatic, it is quite common to switch the order of a sentence: "You are right" becomes "Right you are". In this case "you were caught bang to rights" becomes "Caught bang to rights you were". A more common expression is actually "you were caught dead to rights." "Dead to rights" (or bang to right) is a combination of really old slang from the mid 1800s that is still used today. It means "absolutely", "without a doubt", "undeniably". Usually it implies you were caught in the act. Why did he say "us" instead of me? It's a way of speaking that is used by parents when scolding their children. It implies that not only was the parent disappointed, but so was the child himself. It's like saying "You disappointed me and you disappointed yourself."

To be 'caught bang to rights' is informal British English. It's equivalent to the more widely-known idiom 'caught red-handed'. Both mean to be caught either in the act of a crime, or with unquestionable evidence to connect you to the crime. Not everyone in the UK uses the expression, but everyone understands it. You often hear it in the dialogue of police dramas set in England for example, particularly those involving more working class characters. The word order also sounds natural in colloquial British English, particularly some regional dialects. Wallis is from Lancashire in the north of England, and the emphatic sentence structure 'Caught bang to rights, you were.' (with a pause and a comma) fits his character perfectly. Finally, the 'us' means the two of them. Wallis and Gromit are very much a team. I hope you enjoy Wallis and Gromit films. They're works of genius in their modest way.

I don't think it's odd at all, and I don't think it's outdated. it's just British colloquial speech. But I'm a U.S. native and we would need a UK native speaker to tell us for sure. Synonymous expressions would be "caught red-handed," or "caught with your hand in the till." What it _means_ is: a) You were caught doing something wrong. b) The situation is clear. There's no doubt. It's obvious. c) It wasn't an accident or a misunderstanding. There are no possible excuses. d) You deserve to be disciplined. Why it means that, I don't know and can't explain. An example of how it could be used: "The cookies kept disappearing. Each of our children said the other one was doing it. The other day I caught Jimmy with his hand in the cookie jar. He said 'I was just counting them to make sure Sally hadn't stolen any.' I said 'don't give me that, I've caught you bang to rights.'"