First, you probably want to put the scripts in the OmniOutliner script directory. Easiest way to do this is to go into OmniOutliner, and from the Scripts menu, select Open Scripts Folder -> Open OmniOutliner Scripts Folder (name will be slightly different if you have the Pro version, but I think you can figure it out!). That will open the folder in the Finder, creating it if it doesn't already exist, and then you can move your scripts in there. That way they will only appear in the Scripts menu when you are actually in OmniOutliner as the frontmost application.
For binding scripts to keyboard shortcuts, I like
FastScripts from Red Sweater Software. It's free if you use fewer than 10 shortcuts, $14.95 otherwise.