Is there any difference between these words in terms of their formality, usage and meaning:
deride / ridicule / scoff at / mock / make fun of / poke fun at
Are there any other verbs that mean the same or similar?
That's a lot of words to try to explain.
I will tell you that "derision" is not light-hearted. There's an element of contempt that is not necessarily there if you are just "poking fun" at someone.
You may poke fun at or make fun of your friends. You may ridicule or scoff at their ideas. But you wouldn't deride your friends.