Southampton, chasing their first win at Hillsborough for nine years, were hit by a four-goal blitz in 13 crazy minutes, as the Owls secured their third victory in four games.
Wednesday had threatened early on, Marcus Tudgay going close with a 15-yard shot on the turn before Southampton almost broke the deadlock.
Midfielder Andrew Surman's free-kick found Stern John, who chested the ball down before hitting a low six-yard shot that was blocked by the sprawling Lee Grant.
Wednesday went ahead in the 41st minute when midfielder Whelan threaded the ball to Sodje as the lanky striker burst into the area only to be brought down by keeper Kelvin Davis.
Whelan stepped forward to coolly slot the spot-kick home for his first league goal of the season.
Inigo Idiakez, on at the start of the second half for the ineffective Jhon Viafara, promptly picked up a booking and almost hit the equaliser with a looping strike after his corner had bounced back to him, his swerving shot spinning inched wide of the target.
The Sheffield side added a second goal on 51 minutes, Tudgay slipping the ball inside to Sodje who finished with a low 12-yard strike, before Whelan struck the third five minutes later, his 20-yard shot slipping under Davis after the keeper had parried his shot.
Sodje hit his second in the 62nd minute, a spectacular strike from the edge of the area before Burton O'Brien completed the rout three minutes later, drilling the ball through the legs of the unfortunate Davis.
Idiakez should have scored a consolation goal seven minutes from time when he connected with Surman's cross from the right only to balloon the ball high over the bar.