One officer claimed that members regularly sang a song which includes the words: “Dashing through the Reich…killing lots of kike (Jews).”
The Daily Telegraph has been shown a video of one of the members reciting the first line of the song before a friend silences him, saying, “No, no!”
Matters came to a head this week after a series of emails in which senior members express concerns about the “absolutely disgraceful” behaviour at meetings were leaked to The Oxford Student newspaper.
One officer told the newspaper that “lots of people were singing (the song) that night, and indeed on many other nights”.
Joe Cooke, who was president of OUCA during this year’s spring term, is one of the senior members who have decided to resign.
He told The Daily Telegraph he was quitting “because of the extent of the debauchery” at meetings, where the annual bill for port runs to ￡10,000, the equivalent of a third of a bottle per person per meeting.
“It has become more like a pub than a political association,” he said, likening the meetings to those of the Bullingdon Club, the drinking club once frequented by David Cameron.
“I am committed to the Conservative Party but this association has come to represent everything we’re supposed to stand against,” he added.
The students’ antics are a far cry from the days when the likes of Margaret Thatcher, Edward Heath and Theresa May were members.
At one recent event, OUCA’s returning officer, Tom Hendriks, was photographed pouring alcohol into a pith helmet as another student drank through a hole in the top.
Another picture shows a fancy dress party in which one student is dressed as Baroness Thatcher, while another is dressed as a miner and a third is holding a sign saying “miners love shafting”.
Mr Cooke, 21, who is a former comprehensive school pupil from Barnsley, added that when he spoke at meetings after he first joined the Association “I was ridiculed for my accent…they would say things like ‘ee bah gum’ and create a culture of intimidation”.
OUCA has faced repeated accusations of racism in the past. In 2000 four members were expelled for making Nazi-style salutes and in 2009 Oxford University temporarily banned OUCA from using “Oxford University” in its name after two candidates made racist jokes at a hustings meeting.
James Lawson, a student at St Edmund Hall college and president of OUCA, said: “I haven't seen the video yet and we are investigating to find out whether this was a member of the Association.
"If it turns out this person is a member we will take immediate action to expel them from the Association. Racism has no place in the Association or our society.”
OUCA is the biggest single organisation within Conservative Future, the body for young Tories which is run from the party’s London headquarters.
A spokesman for the Conservative Party said: “Racism of any kind has absolutely no place in the Conservative Party, and we will look into any allegation against a party member as a matter of urgency.”
A spokesman for Oxford University said: “The University Proctors, who are responsible for discipline, have been made aware of the article and will be considering whether there are grounds for further investigation.”
Additional reporting by James Rothwell
William Hague is currently the association's Honorary President (Picture: PA) 
Guy Hands (Picture: REUTERS) 
Theresa May, the Home Secretary (Picture: AFP) 
Sally Bercow was a member during her days at Oxford (Picture: AMELIA TROUTBRIDGE/ EVENING STANDARD) 
Nick Robinson, the BBC's Political Editor, outside No 10 Downing St. (Picture: REX FEATURES) 
Courtney Love, pictured with Kate Moss in 2007 (Picture: REX FEATURES) 
Andy Street, the boss of John Lewis, was a member of the Association (Picture: PAUL GROVER) 
John Bercow, the speaker, met his wife Sally through the association.?Photo: PA
Emma Watson is currently studying at Oxford University. ?Photo: emmawatson.com