Police found them with stab wounds in Park End Street in the early hours.
The victims - aged 20, 22 and 26 - were stabbed at around 3.15am on Saturday.
They were a taken to hospital for treatment.
Officers were called to the scene after receiving a report of an ‘altercation’.
A large scene watch is in place in Park End Street and Worcester Street car park.
A 20-year-old man from Oxford arrested in connection with the incident has been released without charge.
Investigating officer, Detective Inspector Matt Bick, based at Oxford police station, said: “I am appealing for witnesses to this incident, or anyone who may have information about what happened, to please get in touch with police.
“I would also ask anyone who may have dash-cam footage from the local area around the time of this incident to please review the footage in case it may have captured something that could assist the investigation.
“At this time there is a large scene watch in place with both Park End Street and Worcester Street car parks remaining closed.
“There will also be an increased police presence in the local area whilst we carry out this investigation.
“Anyone who has any information can contact police by calling 101 or making a report online, quoting reference 43210329449.
“Alternatively, if you wish to remain anonymous, you can contact the independent charity Crimestoppers on 0800 555 111 or via their website.”
Park End Street and Worcester Street car park remain closed at this time.— TVP Oxford (@TVP_Oxford) July 24, 2021
If anyone needs to contact police about this incident, please call 101 quoting reference 356 of 24/7.