Step 1: Download and install iTunes on the new/reformatted computer
Step 2: Open iTunes and add new songs to iTunes
Step 3: Plug your iPod/iPhone and turn off the auto sync in case that automatically synchronization will erase the content on iPod
How to turn off the auto sync:
(1), Launch iTunes
(2),go to the menu edit–> "preferences on iTunes menu
(3),go to "devices and select "disable auto sync for iPhone and iPod and then go to "ok"
Step 4:Download and install Aniosoft iBackup
(http://www.aniosoft.com/aniosoft-ipo…-transfer.html) and it will detect songs on your iPod/iPhone automatically
Step 5: Transfer all the content from iPod/iPhone to iTunes with Aniosoft iBackup and then iPods original songs are together with new songs on the newly installed iTunes

Step 6: Sync your iPod/iPhone to iTunes where both new songs and iPod/iPhones songs are currently included