Ok, I had this too and it took me a while to work it out .. the pesky track was The Jackson 5 "ABC" and every single time I plugged my phone into the car, it started playing it , used to drive me mad!!!
1). Are the tracks you can't get rid of, part of an album? If so, go to Settings .. iTunes & App Store .. Show all music , then open your Music app and download the rest of the album from the Cloud. Connect to iTunes, select the album , sync , then deselect the album , sync , they should have gone.
2). If the above doesn't work, go to Settings .. General .. Usage .. Storage .. Manage Storage .. Music .. and if the tracks are listed there, delete them.
3). The only other thing I can suggest connect phone to iTunes ... go to the "Music" tab of your phone ... scroll right to the bottom ... and there any "manually added" songs there? If so, are these the pesky hangers-on? Delete them then re-sync.