The confusion started when Japan's Uchimura climbed onto the pommel horse, considered the sport's hardest event.
Oldham made up for his failure in the individual all-around final by taking silver in the men's pommel horse.
The items, found near Bedale in May, include a gold sword pommel, a unique silver neck ring and an armlet.
British men's gymnastics has broken out in London, earning the team bronze as well as the two medals Sunday in pommel horse.
"We already exceeded our expectations by qualifying, " said British captain Louis Smith, a fan favorite because of his pommel-horse mastery and Mohawk-style coif.
The large sword pommel is made from iron and inlaid with plaques of gold foil and is believed to be from an Anglo-Saxon sword.
The King was fighting a counter-offensive against the French in July 1087 when he fell against the pommel of his saddle and badly damaged his intestines.
Louis Smith and Max Whitlock added two medals in the pommel horse, silver and bronze respectively, and Beth Tweddle took home bronze in the uneven bars.
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British fan favorite Louis Smith tied for the highest score in the pommel-horse final but lost a tie-breaker to Hungary's Krisztian Berki, who had a higher execution score.
The Taverham High School pupil is believed to have been injured when she landed head first from a pommel horse on to a safety mat on 12 March.
Smith, who was trained by the club's head coach and Team GB gymnastics coach, Paul Hall, won a team bronze and an individual silver medal in the pommel horse event at London 2012.
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The United States were in silver medal position but poor pommel horse routines from Kei Wen Tan and Raj Bhavsar allowed Japan to finish second after a strong team performance on the high bar.
The agony of gymnast Naoya Tsukahara, whose hopes for an individual all-around medal were dashed last Wednesday when he inexplicably fell off the pommel horse, was obvious as he seemed to sleepwalk through his other events.
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