Should I run if I am sore?

Running can result in DOMS (delayed, onset, muscle soreness), which usually is at its most painful 24 - 48 hours after strenuous activity. If you try to push through DOMS you could end up causing more damage to your muscles. Resting or gentle exercise till you have recovered is a better option if you have DOMS. 

If you have an injury then trying to run through it can be risky. It is always best to get an injury checked by a physio and follow advice on whether you can continue to run. Some injuries you may still be able to run, while others will require a break while you rehab and heal. 

Mild leg pain and stiffness from running is quite normal and provided you are not experiencing intense pain or discomfort once you start running, then you should be ok to continue. Remember to do a warm up before you run, build up your running slowly and seek advice from a physio if needed.