Nerve injury is usually diagnosed through a clinical exam and then possibly with special tests. Most of the time nerve injury will present with specific symptoms - numbness, tingling, burning, radiating pain or sensations. These things are correlated with sensation and strength tests to determine which nerves may be affected.
If there is question regarding nerve function, nerve conduction studies may be done in order to determine if the nerve is working right.
If you have multiple injuries, you should be able to get them all looked at and taken care of with one visit, as long as you talk to your doctor about everything that is bothering you.