As a MOTOR nerve, it supplies:
- Most of the extraocular muscles: inferior oblique, and the medial, inferior and superior rectus muscles.
- Around 2/3 of the muscle that lifts your upper eyelid: levator palpebrae.
It is also joined by PARASYMPATHETIC fibres with run along it for a while. The parasympathetic fibres, via the ciliary ganglion, control the smooth muscle within the eye. They constrict the pupil (pupillary reflex, due to bright light) and increase the convexity of the lens (accomodation reflex, when focusing on a nearby object).
The following is typical of people with a III nerve lesion: on the affected side, the eye deviates laterally, the pupil is dilated, and there is ptosis (drooping eyelid).
- The lateral deviation is due to unopposed action of the lateral rectus, which is supplied by a different cranial nerve
- The pupil dilatation: due to unopposed sympathetic supply to the pupil
- The ptosis is due to loss of the III nerve's share of the motor fibres to the eyelid levator muscle.
Note that the parasympathetic fibres run along the outside of the oculomotor nerve. Therefore, they will definitely be affected in the case of, say, a tumour that compresses the nerve as a whole. However, the middle of the nerve is farthest from the blood supply to the nerve (which also runs on the outside), and so in diseases affecting the blood vessels, like diabetes or hypertension, it is possible to affect just the oculomotor nerve, and not the parasympathetic supply that runs with it. The latter is right beside the blood supply, so it tends to get spared. If this occurs, the pupils will be normal but the rest still applies (and you will be given an important clue as to the diagnosis!).
Obviously, any testing of the ocular movments (e.g. getting them to follow an object with their eyes) will also be markedly off, as all extraocular muscles apart from lateral rectus and superior oblique will be affected by a III nerve lesion.
(The above image is from http://sprojects.mmi.mcgill.ca/braintumor/section1/subsection7/default.htm)