What's the difference between "I am livid", "I am full of wrath" and "I am enraged"?
You will notice, the Merriam Webster definitions seem to be very similar. In usage, I would say there is an order or strength. From weakest to strongest Livid-Enrage-Wrath
Wrath is slightly archaic and invokes biblically retribution and punishment.
the root of Enrage is "rage" https://www.merriam-webster.com/dictionary/rage which has connotations of violence and uncontrollable anger.
Livid, at least where I have seen it used and used it myself, does not have these connotations. In fact, I would expect to see it more used when there was an impotent anger, where the person who is angry knows they can't do anything about it and have to just put up with it. "Daniel was livid when his boss took credit for his idea".