1. In imperative sentences, 不要 and 别 maybe can both be translate into "Don't" in English, for examples,
a. Don't be late !—— I think you can say "不要迟到!" or "别迟到!" interchangeably
b. Don't swim here !——“不要在这里游泳” or “别在这里游泳” interchangeably
2. 不用 can also be replaced with "不需要" or "用不着", which in English can be translated into "needn't (do)", for examples,
a. I needn't go to school tomorrow.——我明天不用上学 or 我明天用不着去上学 or 我明天不需要去上学。
b. You needn't tell me this secrect.——你不用告诉我这个秘密 or 你用不着告诉我这个秘密 or 你不需要告诉我这个秘密。
3. In un-imperative sentences, 不要 may be better to translate into "don't want " or "woudn't like " or , which stands for the person's willing to not do something, for examples,
a. I (don't want to/wouldn't like to) go to Ireland by ship——我不要坐船去爱尔兰 or 我不想/不愿意坐船去爱尔兰
b. Sherry (doesn't want/wouldn't like) this pirated book——Sherry不要这本盗版书 or Sherry不想要这本盗版书
4. 别 seems to be used in imperative sentences generally and I can't think up the other examples at once.