This is a simple(ish) guide to fighting bosses when you are at a clear, unchangeable disadvantage.
!!IMPORTANT!! DO NOT QUOTE ME ON THIS (unless it actually works... which is always)
The only disadvantage you might have here is you are unarmoured and have gained no health. In most cases you are screwed, but if perchance you have a ranged weapon, you may have a chance. Make sure to have a lot of ammo and health potions, dodge all the attacks, and just shoot the hell out of it. If you are low on health, use a potion. If you do get killed, make sure you armour yourself directly after the battle, so that next time, the eye won't be so lucky.
The only way you could be at a disavantage is if you disregarded the Old Man's advice, and fought the Skeletron without proper equipment. You will probably die, and i honestly can't help you because I have always fought it when properly armed, check back another time when i have tested it.
If you don't have the Vilethorn or a Spear , you probably won't make it, but there is still hope. Try your best to listen for the digging sound that the Eater of Worlds makes, when it comes out of the ground attack the head, if you attack else the boss will split, making it hard for you. this might not always work, but the easiest thing to do is to get proper equipment and challenge it when you have a Spear or Flail type weapon.
Posting later (the only advice I have is to make sure you hit all the eyes with a piercing weapon/magic, and run and gun from the main body, Kick him in the nadgers and scarper.)