Michael Dodele, 67, was found dead in November -- only 35 days after his release from prison -- with stab wounds in his chest and left side, the Los Angeles Times reported Monday.
Ivan Garcia, 29, Dodele's neighbor, was arrested by the Lake County Sheriff's Department, which said the suspect made "incriminating comments, essentially admitting to his attacking Dodele."
Oliver has pleaded not guilty to first-degree murder, burglary and elder abuse charges.
The suspect said during an interview that his son has been molested in the past.
"Society may see the action I took as unacceptable in the eyes of 'normal' people," Oliver said. "I felt that by not taking evasive action as a father in the right direction, I might as well have taken my child to some swamp filled with alligators and had them tear him to pieces. It's no different."