Scripts menu
There is a system-wide Scripts menu that appears on the right side of the menu bar. You can turn on the Scripts menu with the AppleScript Utility in your /Applications/AppleScript folder.
Place your OmniGraffle AppleScripts inside ~/Library/Scripts/Applications/OmniGraffle Pro (drop the Pro if you're using the Standard edition), where ~ is your home folder. Then, while OmniGraffle is open, just click the Scripts menu and choose a script to run it.