That's the "Track Bar", sometimes called a panhard bar, but not a sway bar.
Some fella's install an adjustable length aftermarket Track Bar. But if it were me I would just use the bar you have as long as you have tire clearance.
What you are seeing is the nature of the Track Bar design. The axle moves slightly from side to side as the axle goes up and down. This is due to the length of the Track Bar and the fact that it rotating about a fixed point.
In my '65 I have 5" drop springs and I am running the stock length track bar.
I did a technical write up on track bars... check it out here:
http://talk.classicparts.com/showthread.php?t=14368/
