Frank Gallagher often refers to him as "Eddie the Owl", referring either to his fondness for collecting cuddly toy owls (as seen when he moves out of the Jackson household in series 1), the appearance of his face, or both.
Eddie is devoutly religious. He once told Frank that years earlier, he wanted to "work for God in Africa. Big place. Big work". He also expressed shock that Karen once used the C-word "on a sunday".
Eddie caught his daughter Karen giving Ian Gallagher oral sex under the table (a test of Ian's sexuality) and chased Ian and Lip out of the house. This led to him leaving Sheila and though Lip blamed himself, Karen told him that he had been looking for an excuse to end his marriage for a long time. Eddie later punched Frank in the face at The Jockey and told him to pass the message onto his son, but despite this violent start the two shared a friendly drink before Eddie left the estate. It was during this drink that Frank learned that Sheila was half insane, didn't leave the house and was accumulating a large amount of money from her disability benefits, triggering his interest in her that led to their relationship.