By the time he turned two, he had a vocabulary stretching to thousands of words, while most children his age would have mastered only about 50.
Now Oscar lectures his amazed mum and dad about the reproductive cycle of penguins and conducts classical music symphonies as he listens, identifying individual instruments.
His father Joe, 29, is fully expecting the day to come "when he turns around and tells me I'm an idiot".
"Oscar is a child of very superior intelligence," said Dr Peter Congdon, from the Gifted Children's Information Centre in London.
"His abilities fall well within the range sometimes referred to as intellectually gifted. He demonstrated outstanding ability."
Dr Congdon ranked the toddler in the 99.99th percentile, meaning he is one in 100,000 in terms of his intelligence.
Oscar lives with his IT specialist dad and stay-at-home mum Hannah, 26, in Reading, England.
Both parents have normal IQs, although Oscar's maternal uncle, Jonathan Masters, was a child prodigy who began a university degree in computing aged just 13.
"He is always asking questions," Joe said. "Every parent likes to think their child is special, but we always knew there was something particularly remarkable about Oscar."
Assessors at the Gifted Children's Information Centre said Oscar, an only child, is one of the brightest youngsters they have come across.
His intelligence is literally off the scale, with the 45-minute Stanford-Binet test being unable to measure higher than 160.
He will need to be tested further in the years to come to establish his exact score.
Oscar's parents say they encourage him to follow any activity in which he shows interest.
He is already showing a gift for music and has asked for a saxophone for Christmas, despite the fact he is far too small to be able to play.
"He will sit in the back of the car listening to the Indiana Jones soundtrack and he'll be conducting with his fingers," Joe said.
"Then he'll say, 'Here comes the brass with the French horn' and then 'Here come the strings'."
Hannah said that Oscar "amazes everyone".
"We knew at 12 weeks he was extremely bright. He was unusually alert," she said.
"At four months, I would hold up two items of clothing and he would pick out which he wanted to wear.
"His vocabulary is amazing. He's able to construct complex sentences. The other day he said to me, 'Mummy, sausages are like a party in my mouth'."
A spokesman for Mensa confirmed he was the youngest boy to join the society, which requires a minimum IQ of 148.
Mensa UK chief executive John Stevenage said: "Oscar shows great potential. Converting that potential to achievement is the challenge for his parents and we are delighted that they have chosen to join the Mensa network for support."