George Pilkington added a fourth in a devastating first half and Sodje scored his fourth 12 minutes from the end.
Rotherham, looking to build on the victory over Bradford seven days earlier, started brightly with Martin Woods forcing a save from Joe Anyon in the fifth minute.
Danny Whittaker burst forward and unleashed a drive which sailed over Gary Montgomery's crossbar.
But Montgomery was culpable on ten minutes when Port Vale took the lead as Sodje raced in front of the goalkeeper to head home Danny Sonner's diagonal ball.
Ian Henderson tried to spark Rotherham back into life with a snap-shot from 18 yards which Anyon palmed to safety low to his left.
Sodje doubled the lead on 25 minutes after being gifted acres of space to aim and fire home Leon Constantine's cross past Montgomery from eight yards.
He then completed his hat-trick with a powerful downward header from Sonner's right-wing corner after leaving defender Pablo Mills chasing shadows.
Constantine could have added to the Millers' misery when he was played through 12 minutes before the break but he planted his lob on to the roof of the net.
Montgomery at least atoned on 39 minutes when he beat out Whittaker's shot from Malvin Kamara's low cut back.
The fourth eventually arrived on 43 minutes and it was again Sonner who was the architect.
He whipped in a dangerous free-kick which captain Pilkington hammered into the roof of the net from three yards out.
Rotherham could have been given a glimmer of hope on the stroke of half-time but Henderson hit the crossbar and Delroy Facey's rebound was well saved.
Stephen Brogan showed a bit of life with a run and fierce drive which nearly caught out Anyon on 51 minutes.
Vale were buzzing with confidence and Constantine almost stretched their lead even further with an acrobatic effort from Kamara's cross.
Facey gave Rotherham hope on 67 minutes with a fierce shot that beat Anyon after he was set up by Brogan and Henderson.
But Sodje restored the four-goal advantage when he flicked home Nathan Lowndes' left-wing cross.