How do I stop Endnote x4 from automatically putting imported references into BOTH “Imported References” and “All References Folders”? I want to the imported references to go only into “Imported References”.

Are you saying that you do not want everything imported into your library following a search?  If so, you want to use the World and not the Integrated library + World mode in the upper left hand corner, before performing your searches.  In integrated mode any matches in a search end up automatically in your library.  This is the default setting in X4, but once you switch to library only/online search only, this “sticks”.  

All references are exactly what it says, so there is no way to not show records imported into the library in this “group”. 

Thanks; that has solved my problem