It's just kind of hard wrapping my head around even the basics of these Empires which apparently spanned almost 900 years? And then you have the East Holy Roman Empire which somehow differed from the rest? and how do they all relate to the Roman Empire that we all know and love?
There is only one Holy Roman Empire, no matter what Voltaire might say. And that Empire is the one of, later so called, German Nation, founded in the 10th century by Otto the Great and it was more a merged term for the titles of the King of Germany, Burgundy, Italy and King of the Romans. It was no direct successor state to the ancient Roman Empire, but more successor to a successor, namely the Frankish Empire under Charlemagne, who was the first to be crowned as King of the Romans, if I remember correctly.
The East Holy Roman Empire, as you call it, isn't actually called holy. Only Eastern Roman Empire, Byzantine Empire or just Roman Empire, since it was the surviving eastern half of the ancient Roman Empire. The Roman Empire went through some government changes and ended up with a dicephalic Monarchy, with one Emperor residing in the western part if the Empire; namely Gaul, Italy, Iberia, Britannia and Africa (province, contains today the countries of Morocco, Lybia, Tunisia and Algeria); and the other Emperor residing in the eastern part; namely Greece, Anatolia, Egypt, the Balkans and the Near East. And when Rome fell in the fifth Century, only the western part fell, while the eastern part survived until 1453, when Constantinople fell to the Ottomans. So, the relation is that what we know as Byzantine Empire was actually the Roman Empire from the ancient days.