Why does Nightcrawler get called "elf" by the X-Men? I thought he was a mutant human like the rest.
The actual nickname (given by Wolverine) was "Fuzzy Elf". The reason was (from "Appearance" in http://marvel.wikia.com/Kurt_Wagner_%28Earth-616%29) :
His body is almost entirely covered with a fine indigo-colored fur.
It was Chris Claremont's scripting that evolved him into the swashbuckling hero he is today. Claremont stated that he took the idea that Nightcrawler thought "it was incredibly cool to be blue and furry."
Nightcrawler has pointed ears
Here's a card where the "Fuzzy Elf" nickname is stated (if http://marvel.com/universe/Nightcrawler is not enough of a source):
The answer to this is (and you may have to think about it a little) that Rogue and Wolverine call him Elf or Furry Little Elf because he looks like a blue furry little elf. That is the simplest and most straight forward answer I have ever given in my 43 yrs. But this is the answer to your question.