Sodje pounced for the only goal of the night at Boundary Park and the visitors followed up their 3-0 weekend victory against Leyton Orient after holding on under a flurry of late pressure from Oldham.
John Sheridan's Latics are yet to take a point, having already lost 1-0 at Tranmere Rovers, and their best chance came in stoppage time when Vale keeper Mark Goodlad made a superb save from Chris Hall.
Sheridan, who took over from the sacked Ronnie Moore in early June, is trying to bring in at least one striker to solve his problems in front of goal.
Port Vale changed a winning team but they defended well for 90 minutes and had two commanding centre-halves in Mark McGregor and skipper George Pilkington. Sodje's goal was the icing on the cake and continued his impressive run of form since joining from League Two club Darlington during the close season.
Oldham suffered a huge early blow when goalkeeper Les Pogliacomi, on his second home debut after returning from Blackpool, suffered a knee injury. He was replaced by Chris Howarth and the 20-year-old loan signing from Bolton is expected to stay in the team as Pogliacomi takes at least three weeks to recover.
Oldham midfielder Neil Wood shot off target a few minutes later but Leon Constantine fired a better chance well off target from 18 yards.
There were few openings in the first half but both sides raised their game after the break and Gary McDonald's run from 40 yards out ended with a shot which Goodlad grabbed low to his left.
Sodje could have given Vale the lead on 50 minutes when he burst into the left-hand side of the penalty area and lifted his effort two yards over the top.
Jeff Smith was also off target after McDonald again tried his luck from the edge of the box.
The winner arrived on 66 minutes when Smith crossed to the far post and Sodje easily headed in from within the six-yard box.
The busy McDonald had two shots charged down for Oldham but Goodlad sealed the points with a reflex stop from Hall's close-range header.