The Kind for those files (in the Get Info window in iTunes) should say something like
AAC audio file
MP3 audio file
Those are the typical types of audio files that most external non-Apple players can play (and some can only play MP3 audio files). iTunes on the computer is more flexible, and can play other types of audio files. If it says "MP4" or "MPEG-4" as part of the Kind description, then it may be an audio file, but it is not typical AAC or MP3.
I know it will not say only "MP4" for Kind in the iTunes song Info window, so what does it say exactly?
I am thinking that this is a copyright issue that is blocking most songs being played directly from my iPod to any other device via a USB.
MP3 cannot be copy-protected, I believe. AAC can be copy-protected, and Apple previously used their form of "DRM" in the early days of the iTunes Store. Those audio files are called
Protected AAC audio file
for Kind in iTunes. It's possible those "protected" files will not play on external players that are not from Apple.
In the last few years, songs downloaded from the iTunes Store have not used DRM. They are standard AAC files, but they are called
Purchased AAC audio file
for Kind in iTunes. But the bottom line is, it needs to say "AAC audo file" or "MP3 audio file" as part of the song's description for Kind in iTunes. If it does not, it may be an audio file, but it is not a typical audio file format.
Another characteristic of audio file is the "bit rate" used to encode (compress) them. This is shown on the Get Info window in iTunes as Bit Rate. It is possible that the external players can only play song files below a maximum number. So you may want to look at that Bit Rate number for songs that do play and songs that do not play, to see if there is a pattern.