你好洋鬼子。the verb 遇 means meet with or encounter， and 到 ，见，上 follow 遇 to work as complement of result. 1 they all can follow people or animals . 我在上海遇到/遇见/遇上了她！ 2 If we say "meet some difficulty , problem or bad situation " , we can use 遇到 and 遇上, but we can not use 遇见. 现在公司遇到/遇上了很大的经济困难。我们在海上遇到/遇上了台风。 3 when we express "meet some people and the distance is a little bit far" , we use 遇见, and if when we express " meet some people and the distance is very close" , we use 遇到 or 遇上.

遇到和遇见相比There is a kind of not too clear feeling, may just pass by。for example我遇到一只狗。Or for things for example 我遇到了一件倒霉的事。 遇见和遇到相比Have a clear sense of，It is generally about people 我遇见了好朋友比利。 遇上和遇到差不多，But there is an accident，Unexpected meeting。for example我今天去买菜竟然遇上了xxx。

no distinct difference among them. 遇到 is more colloquial. 遇见 is more written language. 遇上 is both acceptable.