Neid means "envy", one of the deadly sins (it's also the last name of the coach of the German national women's soccer team that is competing right now for the World Cup). A Hammel is a (castrated) male sheep or a mutton, if it's dead on the table. A Neidhammel is a person of a rather disagreeable kind, one that habitually feels envy towards anybody who seems to have any advantage. I found it very hard to express this feeling graphically, and impossible without providing some context.
By way of explanation, one may observe that if Hammel is combined with a trait or habit, it can connote a person who makes this habit a defining characteristic. Thus, a Streithammel is a person who loves a Streit ("fight"). But I can't explain why a Hammel is considered a particularly obsessive creature. And yes, the "ei" in Neid (and Streit) rhymes with "eye".
[Source: Wild Things in the German Language: Kindle version | iBook version]
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