The volume on all of the tracks dropped significantly as I select different sound in GarageBand

When you check the Automation curves, as Keith suggested, don't forget to check the Master track as well.

From the Track menu:

• Track > Show Master Track ⇧⌘M

Form the "Mix" menu:

• Mix > Show Automation A

Or do you notice the drop of volume only after bouncing the finished song? Then you may want to check the GarageBand Settings > Advanced as well. Is the Auto normalize option set? try to toggle this option on or off, to see, if it will make a difference.

See if a volume automation curve has been applied.