The path to GarageBand is
/Applications/Garageband the path to the loops should be
On your external drive that is mounted under
/Volumes you should recreate these paths:
sudo mkdir -p /Volumes/_yourdrive_/Applications
sudo mkdir -p /Volumes/_yourdrive_/Library/Audio/Apple\ Loops
Then copy GarageBand to this new location:
sudo cp -a /Applications/GrageBand /Volumes/_yourdrive_/Applications/
And the loops
sudo cp -a /Library/Audio/Apple\ Loops/Apple /Volumes/_yourdrive_/Library/Audio/Apple
Now launch GarageBand from the external drive.
That should work; but still loads all sounds and support files from their default locations.
If it works you can delete GarageBand on your main drive.
Now rename the directory of the loops to anything, a name of your liking.
(like "Apple Loops-bkp")
Only after renaming: Create a softlink for the sounds:
sudo ln -s /Volumes/_yourdrive_/Library/Audio/Apple\ Loops /Library/Audio/.
Launch GarageBand again.
If it picks up the loops you can then delete the previously renamed folder on your main drive.
With the basic set of loops that should have gained you ~3GB.
For the games a similar procedure might be applied, but I do not know the games in question.
The basics of this procedure should be applicable to most programs, regardless of where they are installed by default (although some insist on being installed under /Applications for full functionality). Large support files or libraries are usually especially worthy candidates, often more so than the applications themselves. At least in previous versions of OS X it was important to use softlinks as outlined above instead of (Finder generated) aliases.
A much easier solution to gain space is of course to move your own media files out of the way and to completely uninstall all those games and programs you no longer need.