So, as a native speaker, you wouldn't really say this in every day conversation?
As a native English speaker from the Western US, I would say that "I must go" is very common.
I thought about this for a while, and I think I agree with you. I don't think I'd ever say "I must go" in a normal conversation. Simply reading it, however, I don't find it especially formal.
For interest's sake, in Australia, the more common way of saying this would be 'I have to go' or 'I need to go'. When we use 'must' in this context, we're likely to add 'really': 'I really must go'.
I've lived in eastern and southern US. Although I'm more likely to say "I have to go" or "I have to get going," if I've already said it and someone is insisting I stay, I'm more likely to been say "I must go." It's just more emphatic.
A more literal translation would be "It is upon me to go!" (Perhaps even "incumbent upon me")