First of all, keep in mind that I am unable to diagnose you because I am unable to examine you, this forum is for educational purposes. The symptoms you describe suggest dysfunction of your vestibular system and/or brainstem stem. Vertigo (a sense of room spinning, rocking on a boat or other sensations of your body moving relative to the ground) is caused by disruption of the vestibular systems of the peripheral ear or the brainstem/cerebellum. Ocillopsia (jerking/swing eye movements) and eye misalignment also localize to these areas.
The tests that you have had suggest that you do not have a structural lesion in these areas. MRI with MRA is very sensitive for stroke and vascular disease/tumor that could cause your symptoms. The other tests VEP (visual evoked potential and BAER (brainstem auditory evoked response) test the "wires" connected to your eyes and brainstem (CN VIII pathway) respectively. Additional tests that might help are a Diamox SPECT scan and cerebral angiogram (but I suspect these will be negative as well).
There are other processes that are more likely for your story (and often have normal MRI/MRA) which include basilar migraine, Meniere's Disease or some infectious/autoimmune processes. Basilar migraine has many of the symptoms you describe, and starting a preventative medication such as Elvail 25mg each night will help evaluate for this possibility. Meniere's Disease is a inner ear disease of endolymphatic fluid dynamics, which the mechanism is not well understood, but could account for a good deal of your symptoms. I would also recommend that you be tested for a wide variety of other possible agents as screening tests such as Lyme, ANA, B12, Copper, HIV, Tuberculosis, celiac disease (gliadin antibodies, transglutaminase antibodies), and a paraneoplastic panel.
I would recommend that you see an Oto-Neurologist that can do specific vestibular tests (Electro Nystagmo Gram ENG) etc.
I hope this has been helpful.
Forgot to mention normal EEG. Doctor says he does not see signs of nystagmus, though no formal test done for this.
It's a strange constellation of symptoms, they may not all go together. However, a peripheral neurological problem should be looked at. I would suggest, if you haven't already, going to a neuromuscular specialist who would perform a comprehensive EMG / nerve conduction test looking for myasthenia / lambert eaton or any kind of a autonomic / sensory neuropathy. Perhaps, you need some blood tests sent for some of these, the neuromuscular doc should be able to figure it out. I don't think it's a brainstem stroke.