**Core Concept**
The question requires knowledge of extraocular muscle innervation and the resulting eye movements. The lateral rectus muscle is responsible for outward gaze, and the superior oblique muscle is involved in downward and inward movements. The superior oblique muscle is innervated by the trochlear nerve (cranial nerve IV), while the lateral rectus muscle is innervated by the abducens nerve (cranial nerve VI).

**Why the Correct Answer is Right**
The inability to look up or medially suggests that the superior oblique muscle and the medial rectus muscle are affected. The superior oblique muscle is responsible for downward and inward movements of the eye, while the medial rectus muscle is responsible for medial gaze. The trochlear nerve (cranial nerve IV) innervates the superior oblique muscle, and its dysfunction leads to the characteristic "downward and outward" deviation of the eye. The medial rectus muscle is innervated by the oculomotor nerve (cranial nerve III).

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because the trochlear nerve (cranial nerve IV) is not responsible for the lateral rectus muscle, which is innervated by the abducens nerve (cranial nerve VI).

**Option B:** This option is incorrect because the oculomotor nerve (cranial nerve III) is responsible for several extraocular muscles, including the medial rectus, but not the superior oblique muscle.

**Option C:** This option is incorrect because the trigeminal nerve (cranial nerve V) is responsible for facial sensation and motor functions, not extraocular muscle innervation.

**Option D:** This option is incorrect because the facial nerve (cranial nerve VII) is responsible for facial expression and taste, not extraocular muscle innervation.

**Clinical Pearl / High-Yield Fact**
The trochlear nerve (cranial nerve IV) is the thinnest and most vulnerable of the cranial nerves, making it susceptible to injury during head trauma or surgical procedures.

**Correct Answer:** C.