If you use the manual method to load songs on the iPod, there is no direct relationship between the content of the iPod and your iTunes library. This is dragging songs from the iTunes library to the iPod in iTunes. iTunes is not keeping track of what is on the iPod and keeping it in sync with the iTunes library. So if you add a song to the iPod and later delete that song from the iTunes library, the song remains on the iPod (unless you manually delete it there too).
If you use automatic syncing, you are either syncing the entire iTunes library, or you are syncing a portion of the iTunes library. Because iTunes is syncing, it is not possible to have more songs on the iPod compared to your iTunes library. Therefore, my guess is that you use the manual method.
how can I fix it?
You need to clarigy how you want to fix it... Do you want to get rid of all the extra songs on the iPod that are not in the iTunes library? Do you want to add the extra songs that are missing to the iTunes library from the iPod?
For your second question, you can set up a smart playlist in iTunes that first starts with ALL of your music. Then, you can have it exclude all songs where genre equals Holidays, Christmas, Xmas, etc. To make this smart list more effective, you'd probably need to manually go through your iTunes library and change the genre setting for all obviously holidays songs to something consistent, such as "Holidays." You can do this from the Get Info window, and you can select more than one song at a time. When you are happy with the smart playlist, have iTunes sync from that smart playlist instead of your main iTunes library.