Hello and thanks for researching this very important question!
Strokes, as such, are assumed to be rare in pet cats, but are beginning to be diagnosed more with MRI scans...these are performed under general anesthesia, so many older pets are not healthy enough to be tested.
A number of things can cause a disturbance of the "vestibular" system in the brain, which is responsible for balance, among other things. These conditions include: 1) ear infection, dogs and cats have VERY long ear canals, so a deep-down exam in needed to diagnose this properly, 2) cancer, 3) contamination of the brain with waste products usually handled by young healthy kidneys and liver...cats develop kidney and liver disease to a fairly high degree as they age,
4) generalized infections (like Toxoplasmosis) that can travel into the brain. The chance of more severe problems increases with increased age of your cat. Symptoms of vestibular disturbance include rapid eye movement from side-to-side, inability to stand or walk due to dizziness, nausea and/or vomit (with refusal or inability to eat), spastic head movements, and a tilt in the orientation of the head. Affected cats prefer to lie on one side of the body only.