If you've smashed a demon orb, you should also start getting meteorite ore.  You can make some decent armor out of it (better than any standard ore), but the real prize of meteorite ore is a Laser sword, which has a wide swing radius and works great against Eater of Worlds.  Swing for the head to prevent him from splitting too soon.  

Also with meteorite ore, you can create a few neat guns.  I favor the laser gun, which does low damage but cuts through several parts of the Eater and can be fired rapidly.  This, with the Meteorite Armor and a lot of mana, can help get some long-range damage going.  

Of course...you'll need a proper pickaxe to farm any of this (I believe Gold is required for meteorite ore), and if you feel your Nightmare Sword is good enough, you may be better served using the gold for armor.  

I wish I could remember what it was called right now, but there's also a green vinelike weapon you can get from the Demonite Orbs that works GREAT against Eater.