First, what editing software are you using?
my audio files, from Itunes are seeming to be referenced from the school's server rather than the local disk.
Second, prove it. Disconnect the ethernet cable or turn off the wireless connection, startup you video editing software (which you forgot to mention), and see if it errors out when referencing one of those song titles. If it does, you can stop using nebulous language like "seeming to be".
Third, start iTunes, highlight one of the problem songs, and do a command-I (get info) on the file to see where iTunes thinks the file is. Click the Summary tab if it isn't highlighted and near the bottom you see the path to the file. If it says it is on the server, then iTunes did not copy the file onto your local disk.
I'm not sure of the optimal way to do this, but one way might be to create a local folder and stick the songs you want in it, then drag or import them into you local iTunes library. You might want to first drop the songs from iTunes else the duplicate listing may confuse you and your edit. Also, you'll have to remove the songs from you current edit and reimport them. If iTunes has a way to copy the songs from the server without doing all the above, that may save you from reimporting the songs into the edit.
Lets hope an iTunes expert sees this.