Sway is used to make several o bjects oscillate back and forth on their own axis. You can use it to create underwater grass, or an army of those obnoxious red liquid-filled glass birds!
Just create all the objects you want to animate, then group them to a parent axis, load the group in the Stage editor, then add the Sway FX bar in the Action editor. Sway will make all children of a parent object oscillate; the parent is unaffected. The key is in the grouping: using Sway on a single object will do nothing, since the parent is never affected and in this case, there would be no children to affect.