It sounds as if your dog may be suffering from facial paralysis. Typically dogs present with a head tilt, drooping of the face on one side, the lips may hang down, food and saliva may come out of the mouth and there is often an inability to blink ( and the eye may look red as it can't blink and distribute the tears as normal). Thankfully in dogs they rarely get strokes and this is more commonly due to damage of the nerve supplying these ares. There are many causes: most common being idiopathic (which is the proper term for we don't really know the cause); Deep ear infection, Polyneuropathy ( multiple nerve disease, but you often get other signs too) and brain disease ( again often other signs are involved).
I would definatly get your dog checked by your vet to rule out infection and some of the other causes. Dogs with facial paralysis can usually adapt quite well and I would hope over time should improve. I usually suggest to owners in the long term that if the eye is getting red it should be kept lubricated with artificial tears.