The 21-year-old had to settle for fourth after a good showing ended in controversial style as he appealed the score awarded for his high bar routine.
The appeal was ultimately unsuccessful but his score was still enough to see him pick up the gold medal on the apparatus.
Oldham began on the floor where after a couple of red flags early on he finished well to record a score of 14.250. That was followed by the pommel horse. Competing just after GB team-mate Dan Keatings and immediately before Olympic silver medallist Louis Smith, he repeated his score from the floor.
The Sky Academy Sports Scholar reached the halfway stage with a 14.300 on the rings after a solid routine. An impressive first vault saw him awarded a 15 dead by the judges and only a slight stumble on the landing prevented him scoring similar with his second attempt. His first attempt was enough to see him claim the vault bronze.
A 14.450 on the parallel bars led the Nottingham-born athlete into his final, and favoured, apparartus - the high bar - with confidence and sitting fourth in the standings.
Oldham put in a spectacular routine and after a worrying moment when a mistake on the scoreboard erroneously gave him a 7.900, a score of 14.600 was then awarded to temporarily put him into the bronze medal position. The Sports Scholar and his team felt the difficulty of his routine meant it warranted a higher score and an appeal was lodged.
The outcome became even more pertinent as Daniel Purvis was awarded 14.800 on the pommel horse meaning the Southport gymnast took the silver medal, pushing Dan Keatings down to bronze and Oldham into an agonising fourth, just 0.150 outside of the medals.
Max Whitlock won the gold medal with a combined score of 89.000.