Following Harvey's Vale's opener for the visitors, Sodje levelled the scores in the first half before James McAtee's penalty saw us take the lead in the closing stages.
Sam Edozie scored late on before Sodje grabbed his second to secure the three points and continue our unbeaten start to the season.
City immediately put the pressure on from kick-off, and nearly opened the scoring in the early stages when Cole Palmer's powerful shot was tipped onto the bar by Chelsea stopper Teddy Sharman.
Nonetheless, it was the away side who struck first as midfielder Vale tucked home from close range inside ten minutes.
City were unfazed by the setback, and we continued to pile on the pressure on the visitors, drawing level when Sodje tapped home following Palmer's powerful free-kick.
And Brian Barry-Murphy's young blues could've taken the lead just before half-time when Edozie set up McAtee inside the box, but Sharman managed to get a hand down to ensure the scores were level at the break.
On the hour mark, Edozie thought he was about to give City the lead, but the linesman raised his flag for a tight offside call.
But the breakthrough finally came when substitute Oscar Bobb played in Sodje, who was brought down inside the box, leaving the referee with no choice but to point to the spot.
McAtee stepped up and smashed the penalty home to give us the lead with just over ten minutes to play.
Edozie then added his third when he slotted home in added time, before Sodje grabbed his brace with a well-taken strike to put the result beyond doubt.
How we lined up
Mikki Van Sas was named between the sticks, whilst Brian Barry-Murphy went for a back four of Shea Charles at right back, Finley Burns and captain CJ Egan-Riley at centre back, with Juan Larios named at left back.
Palmer and Edozie provided the width with Sodje up front.
What it Means
The victory sees our Elite Development Squad continue our unbeaten start to the Premier League 2 season, and the 4-1 result takes us top of the Premier League 2 table on goal difference.
Our Elite Development Squad will take on Crystal Palace in a Premier League 2 clash at the Academy Stadium next Saturday with kick-off at 3pm (UK).
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