Zaneta Krokova, 11, and Helina Kotlarova, 12, who were "holding hands" as they crossed the road, died after the crash on Ashton Road.
Four men, aged 59, 48, 38 and 18, remain in custody on suspicion of causing death by dangerous driving.
A fifth man, aged 23, has been de-arrested, police said.
Greater Manchester Police (GMP) said he was initially arrested for the same offence but was now assisting police with enquiries.
Greater Manchester Police said it had identified the car involved in the collision as a Blue Peugeot 807.
The dark blue vehicle, which had evidence of previous damage to its rear window, was found abandoned on Honeywell Lane.
Nigel Whittle, principal of Oasis Academy, Oldham, said the school was "deeply saddened" by the news of the deaths of Zaneta, who was a first year student, and her cousin Helina Kotlarova, a former pupil.
He said: "Our thoughts and prayers are with their families and friends at this extremely distressing and difficult time.
"We are a very closely-knit school community.  As our students return following the Christmas break, I know that they will care for one another, and our staff will be available to offer the support and time necessary as we all come to terms with this awful loss."
He said with the agreement of the Krokova family the school would join together to pay tribute to Zaneta in the coming weeks. A book of condolence would be opened on Thursday, he said.

As first reported by The Express, the settled community in the Hovefields area of Wickford reported hardcore-laden lorries arrive at the weekend.
The lorries were followed by large mobile homes.
Basildon Council said it is aware of "an alleged breach of planning laws". Essex Police has also been informed.
The Hovefield site - which is subject to a High Court injunction preventing further development - is less than three miles (5km) by road - from the Dale Farm traveller site in Wickford.
Dale Farm was Europe's largest traveller site before about 80 families were evicted from unlawful plots in 2011.
Jill Walsh, of the Hovefields Residents Association, said an English Traveller family in five caravans left the site on Friday.
After they departed, she said, a number of large lorries carrying concrete, hardcore and three mobile homes drove down Hovefields Avenue and onto the five acre field at the end of the road.
Mrs Walsh said because of the narrowness of the road one of their neighbours - an elderly couple - had their fence ripped out and shrubbery damaged so that the lorries could get through.
"If the council does not prosecute over this and deal with the situation urgently they will have a Dale Farm II, but bigger."
Phil Turner, leader of Basildon Council, said: "Basildon Council is aware of an alleged breach of planning laws in the Hovefields area.
"We share the frustrations of residents, but the council does not have powers of arrest and must follow the proper legal process.
"As a public body, we must act within the existing legal framework, as set out by Parliament, and this adds considerable time and cost in dealing with such situations.
"However, residents can be assured that the council is taking all appropriate steps to deal with unauthorised development."
Essex Police said it was investigating a criminal damage report involving the fence and has urged any witnesses to contact them.
A police spokesman said: "Essex Police is aware of an unauthorised traveller development on land near Hovefields Avenue.
"We are liaising with the local authority and will continue to monitor the situation."
Police have been given more time to question four men held over an apparent hit-and-run crash in Oldham on New Year's Eve in which two cousins died.
[NEXT_CONCEPT]
Residents have called for urgent action amid claims that a new mass Traveller site is being created at the end of their road in Essex.