War has the ability to teleport. Therefore, it isn't recommended to fight him with some kinds of weapons like Tesla Gun; those weapons that are used for non-moving enemies. Fighting with weapons like the Demon Thrower is better instead. He will teleport every time you hit him.
He is the first of the Four Horseman of the Apocalypse. It was predicted the next would be Famine, though it was later revealed to be Plague.
In the Bible, War is one of the Four Horsemen of the Apocalypse, along with Famine, Conquest, and Death as harbingers for the Last Judgement, although the first one was supposed to be Conquest or later known as Plague.
He rides the Harbinger, which may be a reference to the fact above.