Toph Bei Fong is an ISTP. She relies on her senses for information and is focused on the present. She tackles problems head-on and is able to figure out on her own the logic of how her earthbending power works.
Iroh is an ENFJ. He is very empathetic and highly intuitive. He is able to remain emotionally stable while taking on the emotional burdens of others. Iroh is a fairly typical Mentor type.
Zuko is a male poster-boy for the INFP type. Feelings come first for him, and he has no trouble dropping plans to be impulsive. He's introverted, valuing his alone time, and is very abstract in his thinking ('honor', 'good vs. evil') and is shown through his ability to act as the blue spirit and make astute observations at times. Zuko is an in-depth study of the unhealthy and healthy sides of this type. During Book 1, he's stuck in an inferior grip (only Te functioning), and for most of Books 2 and 3, he's stuck in a dom/tert loop (Fi and Si negatively reinforcing one another, with no input from Ne or Te). He doesn't become a healthy INFP until his HeelFace Turn is cemented halfway through Book 3.
Aang is an ENFP. He is friendly and fun-loving. He is always thinking in new directions and tries to come up with different ways to solve similar problems. He is true to his values of peace, harmony, and non-violence.