First step in diagnosis is to localize responsible lesion, with these possibilities...
Brain stem lesion:
Internuclear ophthalmoplegia: in young people, most common cause is multiple sclerosis; in older people, most common cause is stroke
Ocular motor nerve lesion:
Third cranial nerve palsy: most common cause is ischemia, but expanding or ruptured aneurysm is chief concern. Brain vascular imaging must be performed urgently to rule out aneurysm. Other considerations are neoplasm and inflammation.
Fourth cranial nerve palsy: most common cause is head trauma; in its absence, palsy can result from weakening of congenitally abnormal tendon or ischemia. Neoplasms and inflammation are rare causes.
Sixth cranial nerve palsy: apart from head trauma, most common cause is ischemia. Increased or decreased intracranial pressure, neoplasms, inflammation are other considerations.
Unilateral ophthalmoplegia: usually results from lesions in the cavernous sinus or orbit, including neoplasm, fistula, inflammation, and thrombosis.
Neuromuscular junction lesion:
Myasthenia gravis: can mimic an ocular motor palsy or internuclear ophthalmoplegia; often accompanied by ptosis or other manifestations of weakness, which fluctuates and is worsened by use. Ptosis eliminated by injection of edrophonium chloride (Tensilon) or by sleep or after ice placed on closed lid.
Extraocular muscle lesion:
Restrictive ophthalmopathy: applies to eye movements impaired by scarring, shortening, or swelling of extraocular muscles, most often caused by extraocular muscle inflammation (as in Graves disease) or orbital infection.