What are the tests for neck injury?

Hard to say. It depends on the examination and patient complaints. It could be anything from a simply xray to something more complex such as nerve conduction studies, an MRI or a myelogram.
PE/Xray/CT/MRI/etc. Evaluation starts with history of the injury and physical exam (testing for tenderness, range of motion, cranial nerve exam, motor/sensation/reflexes/limb-position sense, etc). Imaging tests include x-rays (screening for trauma, arthritis), ct scan (more sensitive for fractures), and MRI (best for evaluating discs, ligaments, spinal cord). Nerve conduction+emg can help diagnose nerve injuries.