Cranial nerve (CN) III (oculomotor nerve) is responsible for certain eye movements. It innervates the following muscles: superior rectus, inferior rectus, medial rectus, and inferior oblique. It also functions in pupillary constriction, accommodation, and eyelid opening (via levator palpebrae). CN III is a motor nerve along with parasympathetic function. If there is injury to CN III these functions will be impaired leading to the presentation of the observations in the question stem.  

The ulnar nerves serves the dorsal and palmar surfaces of the hand from the midline of the ring finger over to the little finger (dorsal and palmar).

The axillary nerve supplies three muscles, the deltoid, teres minor, and the long head of the triceps. The deltoid is a muscle of the shoulder and teres minor is a muscle involved in the rotator cuff. The axillary nerve also supplies sensory information from the shoulder joint, and to the skin below the deltoid. The axillary nerve may be injured during an anterior dislocation of the shoulder joint or a fracture of the surgical neck of the humerus. 

The radial nerve supplies the posterior portion of the upper limb. The radial nerve innervates the medial and lateral head of the triceps brachii muscle (the long head is supplied by the axillary nerve) and anconeus. The radial nerve originates from the brachial plexus and consists of fibers of nerves C5, C6, C7, C8, and T1. 

The ankle jerk (Achilles) reflex tests the nerve root S1, S2. Biceps reflex tests roots C5, C6. Brachioradialis reflex tests C5, C6, C7. Triceps reflex tests C6, C7, C8 nerve roots. Patellar (knee jerk) reflex tests the L2, L3, L4 nerve roots.

The pupillary light reflex and ocular accommodation reflex involves cranial nerve II for the sensory aspect and cranial nerve III for the motor application. The jaw jerk reflex uses cranial nerve V for both sensory and motor. The corneal (blink reflex) utilizes cranial nerve V for sensory and VII for motor. The gag reflex utilizes cranial nerve IX for sensory and X for motor. 

The gag reflex utilizes cranial nerve IX for sensory and X for motor. The pupillary light reflex and ocular accommodation involves cranial nerve II for the sensory aspect and cranial nerve three for the motor application. The jaw jerk reflex uses cranial nerve V for both sensory and motor. The corneal (blink reflex) utilizes cranial nerve V for sensory and VII for motor.

The sciatic nerve is a large nerve that runs through the buttocks and down the lower limb. The sciatic nerve innervates skin of the leg, and muscles in the posterior thigh, leg, and foot. The sciatic nerve is derived from spinal nerves L4-S3. The L4-S3 nerve root also supplies the tibial nerve.

L4-S1 is the nerve root for the superior gluteal nerve. Common fibular nerve is supplied by spinal nerves L4-S2. The obturator and femoral nerves are derived from L2-L4.

The femoral nerve is a nerve in the thigh that innervates the skin on the upper thigh and inner leg and shin. It also innervates the muscles that extend the knee (quadriceps). It is the largest branch of the lumbar plexus and derives from spinal nerves L2-L4. The obturator nerve is also supplied by spinal nerves L2-L4.

The sciatic nerve is derived from spinal nerves L4-S3. The L4-S3 nerve root also supplies the tibial nerve. L4-S1 is the nerve root for the superior gluteal nerve. Common fibular nerve is supplied by spinal nerves L4-S2.

The ankle jerk (Achilles) reflex tests the nerve root S1, S2. Biceps reflex tests roots C5, C6. Brachioradialis tests C5, C6, C7. Triceps reflex tests C6, C7, C8 nerve roots. Patellar (knee jerk) reflex tests the L2, L3, L4 nerve roots. The hamstring reflex tests nerve roots L5 and S1.