One way to do this is to ID vehicles at each point. You get best accuracy counts and routes this way because you know where every car comes from and goes to.
ANPR has been implemented on a Pi. See here:
http://www.singaporegateway.com/optasia/imps.html
That's commercial ("under $500") so it probably doesn't suit this application, but you could approach them to see if they would provide software for a community project / beta test site for free.
Another way to do this is optical flow, if you can position a Pi high enough to look down at the junction. OpenCV will run on the Pi and can track motion in video streams.
You could hook up some through-beam sensors across the roads and correlate the signals to estimate traffic flow. I was impressed with these very cheap sensors:
http://www.amazon.co.uk/gp/product/B00A ... UTF8&psc=1
Spec'ed at 15m range they might work across single carriageways if you put sunshields (e.g. black drainpipe) over them.
If you use them in pairs with a small separation you can tell, in most cases, which direction a vehicle breaking the beams is travelling. The two outputs provide a grey code - 00, 01, 11, 10.
Only one bit changes at any time and you can tell which direction the edge causing the transition is moving.
Obviously sensing across single carriageway roads will miss some vehicles if there is stationary or opposite flow traffic blocking the sensor when another vehicle passes.
You may be able to make use of cheap radar doppler sensors like these:
http://www.ebay.com/bhp/doppler-sensor.
The possibility of measuring vehicle speed may be an added bonus.
Good luck!