The phrase "I'm stuffed!" means that your stomach is very, very full. You can use this expression when you've eaten too much food. It's OK to use with anyone - friends, coworkers, clients, family, and so on.
One word of warning: the phrase "Get stuffed!" is a rude expression that you say to someone that you're angry at. So it's probably not a good idea to tell other people that they should "get stuffed". Just use this expression to describe yourself when you're too full.