The victim is a resident of Pahanga village, over 100 km from Bhubaneswar.
The incident occurred when she had gone to a nearby area to attend the call of nature Wednesday night, the inspector in charge of the local police station, Ashwini Sahu, told IANS.
The men dragged her to a secluded place and one of them raped her while the others watched, he said.
Police arrested all four men, including the main offender, a day later on the basis of the complaint lodged by the victim. The four were remanded to judicial custody after a local court rejected their bail plea, he said.
The girl would be sent for medical examination Friday, he added.
In a separate incident, a man was arrested Thursday in Jeypore town of the state's Koraput district for raping an 11-year-old girl.
The 24-year-old offender had allegedly gone to the girl's house and asked for drinking water. Seeing the girl alone, he raped her, local police said.