Yikes, almost sounds dangerous. it could be several things - but if its as bad as you say than it shouldn't be too hard to track down. First off, there is no point in just replacing one control arm - if the ball joint is toast in one control arm, the other side isn't far behind. Second off, if you replaced one control arm you had to replace the control arm bushing (since they are basically impossible to seperate without destroying). So that means you are currently driving around with one garbage bushing and one brand new bushing - that isn't going to help your handling situation.
So here's what you do, jack up the car - get someone to sit inside it and hold the steering wheel. Next go around to each wheel and try to shake it or jiggle it. If anything moves you will know you have a problem. If its not your other control arm, I'm guessing the ball joints in your tie rods are toast, either that or the bearings in the shock mount is gone.
In any event if the car is old and has never had any suspension work you will need to do a bunch of work to get it back to normal, otherwise you will be doing one bit at a time and bankrupt yourself on alignments. So here's the list - replace shocks and all associated hardware. Replace control arms and bushings. Replace sway bar bushings and sway bar links. Lastly replace tie rods. This won't be cheap - about $800, but it will solve your problem.
Sorry, I've been there myself. There just is no easy fix on a 20 year old car when the suspension has been neglected - it is a testament to the strength of the original design that the car lasted this long on original shocks and suspension components.