Pouliot, who signed off on a five-year contract worth $20 million US, is fresh off a career-high 36-point season with the New York Rangers. He added five goals and 10 points in 25 playoff games.
The 27-year-old joins his sixth team in as many seasons. The forward showed a 16-point improvement from the 20 points he collected in the 2012-2013 campaign with Tampa Bay.
Pouliot has also played for Minnesota, Montreal and Boston.
Payne, also 27, is coming off his fourth season with New Jersey during which he scored four goals and 11 points in 72 games.
The six-foot-three, 215-pound rearguard gives the Oilers a right-handed shot from the blue-line.