"J'ai envie de..." is probably more of a statement than of a demand. Like "J'ai vraiment envie d'une glace." = "I'm craving for ice cream."
"Je veux" is used..
- when you want something from someone like in the sentence: "Je veux une glace." = "I want an ice cream." (basically, buy me an ice cream, especially if the person asks "What do you want?" [Qu'est ce que tu veux?])
- when you want to do something. "Je veux partir." = "I want to go." / "Je veux t'aider." = "I want to help you."
"Je voudrais" is more like "I would like (to)". "Je voudrais aller à la plage." = "I'd like to go to the beach." for example.
"Je voudrais" is way more polite because it implies the person to whom you're talking doesn't need to grant your request.