Taking this in stages, initially lets consider only a single front wheel, with no slip in any direction, where we have an accurate continuous measure of both rotational position and absolute angle. In this case calculating current position (relative to our starting point) is a relatively straightforward trigonometry and calculus problem.
Unfortunately we don't know our absolute front wheel angle (unless we are free to equip it with a magnetometer or similar), instead we know our front wheel angle relative to the body of our vehicle. We can effectively define this as a bicycle type configuration, with a pivoting front wheel and a fixed rear wheel. The absolute angle of the front wheel can now be calculated from the absolute angle of the body (equal to the angle of the rear wheel) plus the relative angle of the front wheel to the body. An additional calculation is therefore required to determine the absolute angle of the rear wheel, based on our measurements from the front wheel. This will depend upon the distance between the front and rear wheels (consider the difference in turning circles between a single bike and a tandem to picture this). Again this is a trigonometry and calculus problem, this time in the reference frame of the vehicle.
Extending this to a four wheeled vehicle causes complications, as some of the wheels now have to slip. My mental image for this is two bicycles side-by-side, with bars connecting the frames together, and some mechanism ensuring that their steering is synchronised. If the bars connecting them are short then there is very little slip required. If they are very long (making the bikes far apart) then one or both of the front tyres will need to slip sideways to make tight turns. The distances travelled will also differ between the wheels.
Further physical analysis from this point is likely to get very involved, and will depend upon frictions and masses on each wheel. A practical approach might be to take measurements from the rotation of the two front wheels separately and then average at some point in the equations discussed above.
Further complications arise when rotational slip in any of the wheels on the ground is considered, or if any of our measures are subject to error. To incorporate these would require a very detailed model of your vehicle and a better approach would probably be to fuse an estimate from our simplified analysis above with information from other sensors using a Kalman filter or similar. In this case it may be worth considering what states are estimated in your filter, as including absolute orientation as an explicit state and using it within your calculations may give you a better overall estimate of position. A clever filter might also include an estimate of slip as part of its measurement uncertainty.