Stroke or Transient Ischemic Attack (TIA): The combination of blurry vision, hoarseness of voice, mouth deviation, and mild jaw pain could indicate a stroke or TIA affecting the brainstem or cranial nerves, particularly if these symptoms are sudden in onset. However, the duration of 3 months makes this less likely but still a consideration due to the possibility of a slowly evolving vascular issue or a series of small strokes.

Multiple Cranial Neuropathies: Conditions such as multiple sclerosis, Lyme disease, or sarcoidosis could cause multiple cranial neuropathies leading to the patient's symptoms. The gradual onset over 3 months fits with a chronic inflammatory or demyelinating process.
Skull Base Tumors: Tumors at the base of the skull, such as meningiomas or schwannomas, can compress cranial nerves, leading to symptoms like hoarseness (if the vagus nerve is affected), blurry vision (if the optic nerve is involved), and mouth deviation (if the facial nerve is affected).
Giant Cell Arteritis: Although more common in older adults, giant cell arteritis can cause visual disturbances, jaw claudication, and other symptoms due to inflammation of blood vessels. The hoarseness and mouth deviation would be less typical but could occur if there's involvement of the nerves or vessels supplying these areas.

Lung Cancer with Metastasis: Metastatic lung cancer can cause a range of neurological symptoms if it spreads to the brain or skull base, including cranial nerve palsies. The hoarseness could be due to vocal cord involvement or compression of the recurrent laryngeal nerve by a tumor or lymphadenopathy in the chest.
Aneurysm or Arteriovenous Malformation (AVM): A slowly expanding aneurysm or AVM in the brain could compress cranial nerves, leading to the patient's symptoms. These conditions are medical emergencies if they rupture.
Infectious or Inflammatory Conditions: Conditions like tuberculosis, neurosyphilis, or fungal infections can cause a wide range of neurological symptoms, including cranial nerve palsies, and are critical to diagnose due to their treatability.

Amyotrophic Lateral Sclerosis (ALS): ALS is a progressive neurodegenerative disease that affects nerve cells in the brain and spinal cord, leading to loss of muscle control. Early symptoms can include speech and swallowing difficulties, which might be mistaken for hoarseness or mouth deviation.
Tolosa-Hunt Syndrome: This is a rare disorder characterized by severe and unilateral headaches with extraocular palsies, which could potentially explain some of the patient's symptoms if there's involvement of nearby structures.
Neurodegenerative Disorders: Certain neurodegenerative disorders, such as progressive supranuclear palsy or multiple system atrophy, can present with a combination of neurological symptoms, including those affecting vision, speech, and swallowing, although these would be less common and typically have other distinctive features.