The victim was attacked in Gillians Park in Blackbird Leys at 20:48 BST on Wednesday and remains in hospital with serious injuries to his arms.
One suspect is described by police as a black man, aged about 24, of large build, with short hair.
Another is thought to be about 25 years old, with a ponytail and beard.
Det Sgt Wojciech Spyt said: "We would like to appeal to any witnesses in the area at the time of the incident who may have seen a group of four men running down Dunnocks Way towards Greater Leyes."
A man in his 20s has been taken to hospital after being stabbed by a gang of four men near a children's playground.