"Swaybars" are really a bit of a kludge... what they do is add effective spring-rate under cornering... the theory being soft springs can be used for smooth ride in a straight line, and the "Swaybar" only comes into play when you turn... somewhat correct when you are talking about your father's Oldsmobile...actually a pretty cheap and clever idea.

(BTW the term "Swaybar" falls into the same Marketing Mumbo Jumbo category as calling Dampers "Shock Absorbers"...)

Theoretically, in a racing application, if the main spring rates are set perfectly, a "Sway Bar" is unnecessary, but in the real world, Sway Bars are useful to fine-tune the spring rate for a given car, and turn...

Remember, under static load (e.g. at the apex)...the spring rate (main + swaybar) determines how the weight of the car is distributed between the tires... if the spring rate is biased to the front, the car will tend to under-steer, if to the back, it will tend to oversteer as you are asking one end of the car to handle more than it's proper share of the cornering load.... this is why "adding rear bar" tends to correct understeer or cause oversteer.

Ideally, the main springs should be about 90% right, and the Sway Bars allow the +/- 10% change required to hit the target.

Now don't forget that Dampers ("Shocks") also enter in by managing effective spring rate during "Transients"... these occur when weight is being transferred from one steady state to another... this occurs as brakes are applied and released, steering input is changes and/or throttle is applied... at any point in a turn the instantaneous spring rate is the sum of these three elements, and they change constantly throughout the turn...

Bottom line, if all three of these elements are not tuned to work in concert, the car can end up handling like crap...

The engineers at Porsche, Corvette etc, really sweat this stuff, so if you are modifying the suspension, do a complete package developed by a good tuning shop that is designed for your intended use.