The first one (with no determiner) doesn't really sound very natural, but all the others are interchangeable and you could use any of them.

Listen to Jonathan, not Kaiu. . . . AN ADVICE is incorrect, since ADVICE is uncountable.

"Let me give you advice": This is a bit formal. It means I want to tell you something helpful. "Let me give you some advice": This is more common. It means I want to tell you a few helpful things. "Let me give you a piece of advice": This means I want to tell you one helpful thing. "Let me give you a little advice": This means I want to tell you a small amount of helpful stuff. "Let me give you a little piece of advice": This is like the last one, but even more specific. It means I want to tell you one small, helpful thing. In the USA, people usually say "Let me give you some advice" or "Let me give you a piece of advice" when they want to help someone.

All are natural. Here is a situation where the first one would be my first choice: "Don't take advice from Tom. He is not reliable. Instead, let me give you advice."