British and American slang words for immigrants?

One of the ones I could think up of was offensive, so I wouldn't list it.

Greenhorn
Alien
Floater

There is also "Pomegranate", which is rhyming slang with "Immigrant". This term is shortened to "pommy" and used by Australians to refer to Britons.

"Wetback" is a derogatory term for Mexican illegal "immigrants", not humorous and shouldn't be used.

I have heard the phrase "wretched refuse" used to obliquely refer to poor immigrants. It is a phrase lifted from the poem on the Statue of Liberty, instantly recognizable to any American with a small modicum of education. As such, it actually has a slightly more positive connotation than such a phrase would otherwise have. It probably would only work for immigrants to the USA though.

Generally a term like that is only really needed during an immigration wave. Such waves tend to be centered from one country, so every such term tends to be associated with a particular nationality (usually as an epithet). As such, you will have great trouble finding a word or phrase that doesn't double as a specific racial epithet.

An American term in wide use over a century ago was "wop," or "without papers."

http://en.wikipedia.org/wiki/Illegal_immigration

It referred particularly to Italian immigrants, and there are other, less flattering references to them.