The first thing to check is whether the same songs sound distorted when played by your iTunes Library (on your Mac). If the songs sound distorted in your iTunes Library, the only suggestion I have is to rip new copies from the CDs.
However, if they sound okay in iTunes, but distorted on your phone, check to see whether you have the phone's EQ set to on. If it is on, turn it off and check the same songs on the phone once again. If they sound okay once the EQ is off, that suggests that the EQ may be too much. In other words, if the song is a bass heavy song and you add more bass, that will simply be too much and lead to distortion. It might even be that the headphones that you're using may not be able to cope with the added bass.
I have discovered that one tune in my collection suffers from distorted sound when played through a pair of clip-over-the-ear buds that I was trying. At a push, I can hear slight distortion with other speakers, but these ear buds make it very obvious.
Don't forget though, it may not only be bass, other less bass heavy sounds can cause issues under certain conditions.
If the songs sound okay in your iTunes Library, and the EQ and headphones do not appear to be the issue, try removing the relevant tracks from the phone and then adding them back again. (In other words, if by any chance there is now an issue with the files on the phone, perhaps replacing them with new "copies" from your computer might solve the problem.)