Hello Ajlabs,
Thanks for participating in the Apple Support Communities.
If your iPod classic only plays music out of one channel, you can get service at the link below. Be sure to try these tests first to isolate the situation to the iPod or the headphones:
Connect the iPod headphones to the sound output port ("speaker jack") on your computer or another audio device that has a 3.5 mm stereo headphone jack. If the issue with the headphones is still apparent, you can request replacement headphones from the iPod Service Website.
If the issue with your iPod headphones is not apparent on another device, try connecting a different set of headphones with a 3.5 mm plug to your iPod. If the issue is apparent with these headphones on your iPod, you can arrange to have your iPod repaired at the iPod Service Website.
From:
Troubleshooting iPod's headphones
All the best,
Jeremy