WARNING: You better have permission from the school to do this!!! If you do this without permission you could get in serious LEGAL trouble. Getting expelled might be the least of your problems.
grc.com has a project called shields up it will do a basic inbound port scan.
Also I think your confusing inbound and outbound traffic. The ports you listed are legit inbound ports but not used outbound for outbound traffic. When a browser connect to port 80 on a web server the web server automatically changes the outbound port to a random one so the web server can accept the next connection on port 80.
If you can disconnect them from the internet for 30 minutes or so you can connect a laptop to the server directly. Before you do that load and learn how to use nessus. Make sure to have a static IP on the same subnet on the laptop as on the server. After that hit the server with nessus. It will even check for vulnerabilities in your web server and other internet facing software.
Then reconnect it to the internet. You now have a list of thing to fix, or not.