How do I delete songs of my iPod using iTunes?
This may vary slightly depending on what type of iPod you have, but generally if you want to delete arbitrary songs on the iPod (without having to modify any playlists etc. in iTunes itself that you are syncing from), you need to have the device set to "manually manage music" on the device Summary tab. Then, you select the device from the top bar when it is connected, and open the "Music" tab, and you can select and delete songs from the list.
When your iPod touch runs low on memory, problems like slow speed, crashing of the device, etc. are very common. Deleting content, like songs, from your iPod touch can be an excellent way to tackle these problems. You can delete songs directly from iPod device, or remove tracks via iTunes or other iTunes alternative.