I think if, in the Music app, you go into an album and individually Delete from Library every song you don't want to see, then it won't pop back up again. At least I haven't seen the ones I've done that to pop up again in my Genre playlist. But I'm not sure I just haven't hit a condition where Apple deems it fit to download (or stream?) everything again. Even though I have deselected every form of Automatic Download I can find.
Of course I'm just the owner of the device, so how could I possibly know what I want my device to do?
I have decided that rather than spend my time deleting songs from both iTunes and my iPhone (since apparently just doing it on iTunes means nothing to the iPhone), it's just best to never buy another song, or anything else, on iTunes ever again.
I so glad I bought an iPod nano shortly before they stopped selling them. It -- get this! -- plays my music. Not stuff I deleted because I didn't like it. The wonders of technology.