Have you tried launching the applications from a different user account? If they behave well there, it's a strong indication that the issue lies in the applications Preferences files in your main account. The cure is to remove those files and let Numbers build a new, clean, set.
Quit Numbers, then, in Finder, press and hold the option key as you go to the Go menu and choose Library. Then follow the path below:
Library > Preferences
Select and delete the file com.apple.iWork.Numbers.plist
I created a new user and logged in as that person. Numbers came right up and behaved normally so I went to Library > Prefrences and deleted all of the com.apple.iWork.* files since I'm having this issue in all iWork apps. I then also went to Library > Caches and deleted the com.apple.iWork.* files there also. Everything works on the new user account by my main account still won't launch numbers without it hanging.
Ok so I'm not sure what is going on but I found this discussion and it helped me. It seems that syncing Documents and Data somehow is hanging iWork apps.
If anyone understands why this is I'd love to know,