+/- POC glucose, CBC, and other labs depending on suspected diagnosis
+/- LP after negative neuroimaging if suspect subarachnoid hemorrhage or meningitis.
Head CT if traumatic, suspect stroke, or subarachnoid hemorrhage (rare).
MRI is study of choice, although there no increased yield from MRI vs CT scan.
Fourth nerve palsy
Increased intracranial pressure 
Third nerve palsy
Vascular:  Stroke, subarachnoid hemorrhage, aneurysm 
Sixth nerve palsy
Neoplastic: Tumor in the subarachnoid space
Ulnar neuropathy
Degenerative/deficiency: Vitamin B12 deficiency, Wernicke-Korsakoff syndrome