What you are describing could easily be a combination of bent and/or worn out parts. The 1st alignment shop was derelict if they couldn't find a problem but still gave you the car with a pull. When it comes to the steering on Volvos (or any car that has some modicum of handling ability) there isn't any such thing as "not that bad" -- it's either good or it's not. There should not be any play in the 240 steering system. Ball joints should be tested by both prying between the strut tube and lower control arm -- AND -- squeezed with big water pump pliers in the same location--no play allowed. There should be no play in the inner or outer tie rods--and the outers should be squeezed like I described for the ball joints.
When you car was sideswiped the other car may have smacked a front tire/wheel--or pushed your car into a curb on the opposite side bending something--even a lower control arm--or frame!
You need to bring the car to a shop that is not the original one and have a thorough examination. I can understand not having the money to make a proper repair--but the 1st shop should have at least found the source of the problem.
And all of that being said, a bad tire can cause a pull--as I found out after replacing a strut, lower control arm and having the frame given a "pull" on my wife's Saab after hitting a huge pothole. Moving the tire changed the pull. Boy did I feel dumb. -- Dave