- Try cleaning out/blowing out the headphone jack. Try inserting/removing the plug a dozen times or so. already suggested
Try the following to rule out a software problem
- Reset the iPod. Nothing will be lost
Reset iPod touch: Hold down the On/Off button and the Home button at the same time for at
least ten seconds, until the Apple logo appears.
- Reset all settings
Go to Settings > General > Reset and tap Reset All Settings.
All your preferences and settings are reset. Information (such as contacts and calendars) and media (such as songs and videos) aren’t affected.
- Restore from backup
- Restore to factory settings/new iPod.
- Make an appointment at the Genius Bar of an Apple store. Seems you have a bad headphone jack.
Apple Retail Store - Genius Bar
If not under warranty Apple will exchange your iPod for a refurbished one for this price. They do not fix yours.
Apple - iPod Repair price
A third-party place like the following will replace the jack for less. Google for more.
iPhone Repair, Service & Parts: iPod Touch, iPad, MacBook Pro Screens
Replace the jack yourself
iPod Touch Repair – iFixit