I have an old set of setup string fixtures that I got with my car. Trying to make sure I use them right. These are the type that are made from 1x1 steel square tubing. I think I figured out how they go on the car. But when I measure from the strings to the center bolt on each wheel, the measurements are not the same side to side. I am off by 5 to 8 mm. Based on these measurements, the square formed by the strings is not aligned with the vehicle centerline. I think. But there does not seem to be any way to adjust the strings side to side (except maybe by bending the steel tabs that register against the frame on each side). Am I making the right measurement when I measure to the center of the axle bolt on each wheel? Should these measure the same side to side if the strings are set right? Has anyone dealt with this issue?

Measure from one of the frame rails in both the front and the back on the same side to the string. Move string in or out until you get equal distance (parallel to the frame), that is making the assumption that yours will let you move string parallel to frame. Hopefully the frame is not bent. Lock the steering wheel in place and centered with a vise grip or some other means. When you get the string equal distance front to back off of the frame rail, measure toe. Left to right doesn't realty matter(within an inch or two) as long as the string is parallel to frame.

I wonder if you are getting a difference because when you go off center on rear you are on axle shaft and the front you are going to the hub retainer bolt head. They are not the same. Axle sticks out further and would be shorter distance to string. Frame rail and if you have a hard time because the string is in between frame rails hold a board or something from top to bottom rail to give you a straight line to string.

Also when you measure from frame to string (again the goal is just parallel on each side... distance from string to frame doesn't matter), make sure that the string is roughly the same height from front to rear. If you're a lot higher on one end, you'll get a bigger difference when measuring from the lower frame rail in front and back.

Here is the way that I do "String the Car"

First rule is to make sure the the distance beteen the strings is the same front to back. Do not worry about the car frame yet. The distance must be exact. You can measure this off the car.
Second. Mount the bars on the car and measure the distance from either the left or right frame rail to the string. I took the wheels off the car to do this. You must get theis exact. To adjust you have to move the bars not the strings.
Third. You are now ready to "string the car"

Helpful tips-
1. Make a fixture to lock the steering wheel or shaft in place. This is so you can get repeatable setting. If there is play in the wheels after locking the steering, find the problem and fix it.
2. If the strings pass through the centerline of the wheels you will get the most accurate measurements.
3.If you put turn plates under the wheels it will be easier to adjust the toe.
4. Roll the car foreward and backward after final adjustments and recheck.

Good point by Bob that I'll reiterate and modify...
4. Roll the car forward and backward after *every* adjustment before measuring.

Set tire pressure at 30lbs.

Something else I do is check the run out on the wheels where your intend to measure. I have welds and they are off by .020 in some areas. If you are doing 1/16th perside in the back that is .0625. So .020 can mean a 30% error and effect repeatability of your measurments as you roll the car arouind.

Bolt the wheels on, jack up the car and place a dial indicator on the rim. Spin the wheel back and forth until you locate 2 areas on oppsite sides of the wheel where the run out is the same and mark them.

Now when you are rolling the car to measure, place the marked areas along the string and you will get the same measurment every time.

Then I go out on the track and hit something hard for the final fine tuning!

torque the lug nuts.

A variation on Lee's technique is just use one point on the wheel but roll the car forward or backward 1/2 a wheel revolution when taking measurements.

You can make a simple, repeatable steering shaft lock with a flat piece of steel or aluminum strip and a long skinny screwdriver you insert through an open steering shaft adjustment hole and then into a hole on the metal strip, which is fastened to a couple extra mounting points you drill into the frame rails. The metal strip runs across the footwell, perpendicular to the steering shaft.

Be sure to measure and position all this stuff after you have the toe set equally on each front wheel and with the steering wheel set straight ahead.