These three forms all express a strong emotional reaction, usually admiration or astonishment, at the degree of something. They are often used in exclamatory sentences. The nuance differs: なんという is slightly more formal and literary, often used with a noun to say 'what a ~'. なんと is also somewhat formal, used before a noun or nominalized phrase (often with ことか/ことだろう), and often appears in written narratives. なんて is more colloquial and can also carry a sense of personal feeling, sometimes even slight contempt, depending on context. All are common in exclamations where the sentence may end with だろう or でしょう, or with a particle like か, but they can also stand alone.