Deleted songs return to iPhone

I know this has been discussed before, but my problem seems to have some unique features. I have an iPhone 6S and the latest version of iTunes. There were dozens of songs on my phone that apparently live in the cloud (I don't use iCloud for my music). Some may have been free songs of the week, but there seems to be an awful lot more than I ever downloaded that way. Some I want to keep; others I don't. I've gone through them song by song and done one of two things:

1. If I don't want to keep a song, I delete it from my iPhone and from iTunes (where it lives in my iTunes Media/Music folder as an mp3 file).

2. For songs I want to keep, but want to remove from my phone, the process is more complicated. Since none of these songs are checked in iTunes, and therefore don't go away when I sync my phone, I've manually moved the files out of iTunes Media/Music into another folder. Then I delete them from my phone and sync. Then I re-import the files into iTunes. Keeping them unchecked leaves them in iTunes and off my iPhone.

HOWEVER, last night, all of the songs, from both these categories, reappeared on my iPhone, even those I had deleted from my phone and from iTunes. Also, in my Edit/Preference/General, there is no checkbox for iCloud Music Library. How can I delete the songs I don't want and keep the ones I want without having to keep them on my phone?