This is where having a clone backup can help set things right.
Now the up side is, if you haven't used anywhere near your half your hard disk storage, there is a trick, you can do to restore things back to normal without getting a migraine.
1. Clone backup your machine*:
http://www.macmaps.com/backup.html
2. Dismount, and disconnect the clone.
3. If your Mac came out before Yosemite, you may be kind of stuck, because Apple no longer makes Yosemite available for new downloads. Calling AppleCare, you may be able to request it become available for your purposes on the Mac App Store (tell them you want it on your App Store for an erase and install). You do not want to upgrade to El Capitan, without taking a look at this:
http://discussions.apple.com/docs/DOC-8811
If you are able to get Yosemite available, the following steps apply:
4. Command-R boot to erase the internal hard drive, and reinstall Yosemite
5. Install the 10.10.5 combo update:10.10.5 Combo and the 2016-001 Security update
6. Repair permissions with Disk Utility.
7. Connect the clone backup and use the Migration Assistant to import back the data on there.
8. Repair permissions again.
9. Test the applications on the system.
If you are not able to get Yosemite available, and you are not ready for El Capitan, do not
4. Delete all malfunctioning applications.
5. Repair permissions with Applications -> Utilities -> Disk Utility
6. Run the 10.10.5 Combo and the 2016-001 Security update
7. Repair permissions with Applications -> Utilities -> Disk Utility
8. Reboot.
9. Run the migration Assistant on your clone backup.
10. Repair permissions with Applications -> Utilities -> Disk Utility.
Hopefully by now the applications should work fine. If not, you may have a system maintenance tool that might be messing up your permissions even more. http://www.etrecheck.com/ can tell you what is installed, and if you have something in the background that shouldn't be there. Copy/paste its results to here, and we can help tell you if you don't want that tool.