School wide projects get students and staff involved in one common activity, promoting unity. A school wide essay or short story contest can end with an assembly in which everyone attends. Or, make a school quilt in which each student makes one square. The finished quilt can hang on the wall in the cafeteria.
A pep rally by its very nature promotes school spirit. Organize pep rallies before big football or basketball games at school. The week of the pep rally, encourage students and staff to dress in school colors. Have art classes make pep rally posters to hang up around school and give extra credit to students who volunteer to participate in the pep rally.
Giving back together is a good way for students and staff to form positive relationships together. Have a charity drive, such as a clothing drive or canned food drive for the homeless. If the school works together toward a common goal, bonds will be made.
To foster good relations between students in different classes, organize some events where the kids can get to know one another. You can arrange a weekly reading group in which classes of the same grade level meet to read aloud together. Or, organize sports games during PE in which classes mix to make up the teams.