"Amis" would be used to refer to Americans; its slang for American. It was wholly meant to be derogatory, much like the older WWI practice of calling Germans "The Hun", or referring to the Japanese as "Japs."
Mega-Edit: Okay so, perhaps predictably, this thread exploded way off course. For those entering it late, the post-graveyard is the result of quite a bit of miscommunication, far too many anecdotes for the sub's tastes and the question of sources. Since digging through a graveyard is both macabre and time consuming, I'm going to try and condense it for people who stumble upon this disaster.
2)The "Psychology" behind such nicknames is explained eloquently and succinctly in this post by /u/devilinmexico13. There are so many people in the course of the thread who are mentioning the nicknames viz. modern standards. Please recall (a) "No current events -To discourage off-topic discussions of current events, questions, answers and all other comments must be confined to events that happened 20 years ago or more, inclusively (e.g. 1995 and older)." (b) The question was in relation to World War Two; its all well and good what you feel is derisive or not in 2015, but that is not the scope of this question nor sub. (c) We're always interested in what you have to say, but please avoid personal anecdotes. Its a trap that's hard to avoid and I was guilty of it much earlier in this veritable boneyard.
3)Finally, the origins of the terms "Nip" and "Jap" and their racist undertones in relation to the war effort of the United States are explained - with sources! - here by /u/Purpleclone
Thank you.
I am not aware of any really popular nicknames for Americans, however, British soldiers were usually referred to as "der Tommy" (plural: "die Tommys") and Russian soldiers were usually referred to as simply "Iwan".
The only "nickname" - if you want to call it like that - for Americans at the time (and even today) was "der Ami" (plural: "die Amis"), which is simply short for "der Amerikaner" (plural: "die Amerikaner").
Tangentially, I never thought Jerry was particularly deragatory, since we (at least in the U.S. and I can only assume in the UK since they coined the term) still use "Jerry Can" to mean one of those 5 gallon fuel containers.
so, i looked it up. here's a supporting piece of evidence stating that likely came from the shape of their helmets resembling a chamber pot. so, I can see how it would be a slur. But, then why is 'Jerry can' still not seen as offensive?
Where did "Jerries" come from? I've never actually heard that word until today, other than when I was working on a project with two guys named Jerry.
Also, holy hell, what bomb went off in this thread?
TL:DR Enough already! The mods have had to delete 164 comments and counting in this thread which is crazy even for AskHistorians.
Please do not post unless you are an expert and can provide sources. Not some random thing you heard in a pub once. Not a quote from a movie. Not a racist joke. The racist jokes will get you banned.
Also; to my German friends. We get it! "Amis" can be used in the modern day as a friendly term of endearment! Thank you for your keenness to participate but do not post this. It breaks our rules and we've deleted over thirty of you so far. The OP asked about insults in conflict. Awesome that a prior slur doesn't mean that anymore! But we really do want to talk only about situations of conflict. We appreciate your understanding.