I suddenly cannot open any files in Script Editor.app

Personally if it was me, I would run disk utility app on my system first.. Then I would reboot and see if that fixes the problem. If that did not fix the problem, I would then go to /Users/your short name/Library/Preferences/com.apple.ScriptEditor2.plist. <—- and delete that .plist file, then reboot and fire up the script editor app to see if the problem is fixed. You may want to make a backup copy of that plist file before you delete It.

I'm not quite sure if that file is hidden in the system, So you may have to unhide hidden files before you can find that plist file

This is the script I use to show hidden files in the system...

do shell script "defaults write com.apple.finder AppleShowAllFiles TRUE\nkillall Finder"

An alternate solution would be trying to restore that .plist file using Time Machine