What should I call algorithms with non-linear non-constant time?
As mentioned by Bryce Kille in the comments, superlinear is what you are looking for. From Wiktionary:


  
  (mathematics) Describing a function that eventually grows faster than any linear one
  


(By the way, the first phrase in your question strikes me as rather odd: "[...] I want to refer to a group of algorithms that are mostly polynomial-time, but one of them is of complexity $O(N \log N)$." Do you simply mean "linear" instead of "polynomial-time"?)