@fullspiral If you don't want the decorations on your neighbors homes at all, set the holiday decorating theme to none for your holidays*, this is what determines neighborhood decorating. You can still decorate your own home using the "attic stack decoration boxes" (I think that's the right name).
To remove left behind decorations make another holiday, all you have to have is a name and an icon, I generally go with something lame like "clean up", set the decoration theme to none, don't add any traditions, and untick the box for stay home from work/school. When the holiday rolls around the decorations will disappear from your neighborhood, you won't have to complete any goals, and your Sims will still attend work & school.
*ETA: This applies to the pre-created holidays as well like winterfest and the like. If edit them and set the decoration theme to none, your neighborhood won't be decorated, but you can still jazz up your own house. :)