Yes, you can delete songs off your iPod without syncing it to the computer by first plugging in your iPod to your computer. Once iTunes opens up, you will see your iPod located in the left panel. Click to highlight your iPod and you will see information on you iPod. On the main screen "Summary" scroll down until you see "Options." Check the box that says "Manually manage music and videos." You will get a pop up asking if you are sure you want to manually manage music on your iPod. Click OK and now you are able to manually delete songs off your iPod without syncing with your computer.
The only way to delete your media without connecting to iTunes is if you have one of those apps that allow you to download from your iPod, the app gives you the option to delete what you downloaded from that app.