How Can You Tell If A Cat Has Had A Stroke...or Been Poisoned?

Different toxins result in different clinical signs.  Toxins can attack the neurological system, the gastrointestinal system, the liver, the kidneys, muscular system, the blood cells, and localized tissue.  Certain toxins like anti-freeze toxicity result in specific clinical findings or signs on lab work.  
Vascular events or "strokes" usually result in neurological problems--altered mentation, difficulty walking, etc.  Metabolic disease can result in symptoms that mimic stroke; trauma is another rule out as well.
This cat needs veterinary medical attention regardless of whether a stroke or toxin is responsible.