My own summation of stropping, based on my somewhat limited experience and what others here have said is:
Stropping can be used to do one (or more) of three things to your edges:
1) Straighten a rolled or otherwise non-straight edge of the edge on the bevel if it was previously very straight and correctly formed.
2) Refine an existing edge to a finer level of finish.
3) Assist in removing burrs, burr remnants, or wire edges on the edge bevel itself.
The stropping medium used, whether some kind of abrasive compound is used, the compound abrasive composition, and the fineness of the compound will all determine which one or more of these will take place and to what extent.
Newspaper on its own on a flat surface will probably have little abrasive qualities and would probably just accomplish #1 above.
Hard felt w/ or w/o compound is used by many to accomplish #3 and also sometimes #2 as well. Sometimes both at once.
Hard balsa w/ a compound could definitely accomplish #1, #2 and possible #3 as well.
Nanocloth is used specifically to have little to no effect on it's own, so that just the compound influences the stropping effect. This is probably accomplishing mostly #2 and some #1.
I know TAZ (Tim Johnson) strops on leather to help deburr. He has success doing this.
I think you'll find that different people often obtain similar results and accomplish similar things using a variety of stropping mediums and compounds. That's clear as mud - ain't it
This is my take on stropping. Feel free to tell me I have it all wrong and then please enlighten me on your interpretation of stropping and it's effects