There two ways to start and complete this quest, however, both ways have the same difficulty to complete, and they're both easy. If you talk with Odgen first, but hand the sign to Snotspill, when you come to talk with Odgen again he will thank you and make a joke about that "magic sign". And will regret about his lost sign. Giving back the sign to Odgen will net you a better item than giving it to Snotspill. Note: you will have to talk with Snotspill to open the chest. Otherwise, you won't be able to open it, as the character says: "I cannot open this, yet".
Method 1
When you reach dungeon level 4, go back to town and talk with Odgen. He will say something about noises on the night and some shadows that look like monsters in town. When he woke up, his sign from the Tavern of the Rising Sun was missing. He will simply ask you to find it and bring it back to him.
Go back to the dungeons and seek the stairs to level 5, and you'll find a unique Fallen One demon called Snotspill guarding it. Just go through the door on the other side (close to the stairs). Kill the fat demons that guard the sign. Grab it and take it to Odgen. He will thank you and hand you the unique item: Harlequin Crest. When you backtrack to the dungeons, talk with Snotspill and he will open the way to the stairs together with a horde of Fallen Ones. Kill them easily and continue your journey.
Method 2
Instead of talking with Odgen just talk with Snotspill, and he will say something about a "magic sign" that has been stolen by those fat demons and only will let you go through if you give it back to him. Like in Method 1, kill the demons and grab the sign, but this time hand it to Snotspill and he will betray you. He'll open up the way together with that Fallen Ones' horde, so kill them all easily and make your way.