^ Front or rear sway bar? Not all cars in the '80s had them, sometimes a base model or even the median model wouldn't while the sportier model would.
Do you feel the excessive sway progressively got worse or is this a sudden change? I mean if you were okay with it in 2005, and now 13 years later... something still there is the problem then, not the lack of a sway bar.
While the sway bar is the biggest factor, the cumulative effect of other things like worn out strut mounts, ball joints, control arm bushings, even under-inflated tires, can add up.
I too would want to add the sway bar(s) but you could have a more serious problem that needs fixed to make it safe to drive, though this late in the game, how much to do to a 30 year old car that was worth little when brand new... would not be much unless you're really attached to it.
Regardless it should be safe if it's going to be on the road, and besides the struts/mounts, the other parts are fairly inexpensive to DIY replace, as would be a sway bar and mounts (get new end links and bushings) from a junkyard if you can find them.