Oasis, You should only go to the underworld if you have at least have shadow/jungle/necro armor. gold armor is needed for molten armor so don't sell it, put it in a chest for later.
Tips for Eater of Worlds: The eater of worlds can be summoned by smashing 3 shadow orbs (There is a bug that sometimes he shows up if you break 2 with dynamite.) or making worm food, Witch is made at a demon alter with 15 rotten chunks and 30 vile powder.
You must fight it in the corruption or it will kill itself if you try to leave with it without dropping anything, Using worm food outside the corruption will kill you like the looking eye.
It is the fastest brrowing AI worm then any other worm and can jump quite high if it rams you from under on the surface, Avoid the head of it at all costs because it does the most damage even in gold armor.
The body's of it are about 150 HP each and it will spit into smaller worms if you kill a part of it but wont if you kill the tail or head, The more worms, The more difficult the fight.
The best weapons to use againest it are:
Ball O' Hurt/Blue Moon/Sunfury
Aqua Scepter
Blade Of Grass
Dark Lance
Vilethorn
In version 1.0.3, The eater of worlds will drop a piece of shadow armor once defeated. However, In the 1.0.4 patch it was removed.
It is best to fight it on a high platform not too high above the corruption or in the cave's where shadow orbs are found, The hunter potion is very useful in this fight so you know where it is even it's in the ground so you can dodge it easy.
Each part you kill drops some demonite ore and some shadow scales witch is used for some dark items such as shadow armor. Once all parts have been killed, The last part will drop some lesser potions, Alot of shadow scales and demonite ore.
You can only get shadow scales from the eater of worlds and each piece is worth 1 silver.