Here's what you need to do...
1.) When you plug in your iPod, iTunes should automatically start. It may ask you install updates or ask you if you want to sync your iPod with iTunes. Don't worry about the iPod updates but sync if you can. If it doesn't sync automatically, you can navigate to "File" on iTunes and use the sync option.
2.) Navigate on the left side of the screen once iTunes detects your iPod. For instance, mine says "Josh's iPod" because that's what I named it. When you have that highlighted, there should be a few tabs on the main part of the iTunes screen. I have an iPod Touch so it might include more but right now I see "Summary", "Music", "TV Shows", "Podcasts", "Photos", and "Info".
3.) If you go to the "Summary Tab" you should find a check box that says "Manually Manage Music and Videos". Make sure this is checked. Without this option being checked, you cannot just go to the songs in your iPod and delete them at will. I'm assuming you have to delete them your iTunes folder and then resync your iPod. Using this option, you can now highlight any song you don't want on your iPod and just delete it and, assuming you have your iPod propoerly connected, should automatically take them off your iPod.
I did these steps on my iPod touch and it worked for me. Let me know if you are still having problems.