Sodje, playing against his elder brother Sam in the Pompey defence, opened the scoring in the 40th minute with a near-post header from a left-wing cross by Callum Kennedy.
After Liam Walker had levelled for the visitors on the stroke of half-time with a stunning 30-yard free-kick, it was Sodje again who popped up with an 85th-minute winner for the Iron with a header from another high ball pumped into the box by Kennedy.
Laws said: "Akpo has not been feeling very well and we considered leaving him off at half-time. But he wanted to go back on and so we dosed him up with tablets.
"When we lost at Crewe on Saturday, Akpo missed three good chances, but he has scored both the chances that came his way and hopefully that will do his confidence a world of good because he is very much a confidence player."
It was only Scunthorpe's second home win of the season - their first since September 20 - and lifted them back out of the bottom four.
Laws added: "It was a huge win for us. This was probably our biggest game of the season. It had been built-up as a 'must-win' game and the players were under real pressure.
"I have to admit we didn't play well but what really pleased me was the way the players dug in and kept going, knowing we could win, even without being at our best.
"We can play better, but we'll not get many more important results than this."