Newdow and other atheists and agnostics also want to stop the use of prayers during the inaugural celebration.
Newdow, who lost a Supreme Court battle to get the words "under God" taken out of the Pledge of Allegiance, has failed in similar challenges to the use of religious words and prayers at President George W. Bush's inaugurations.
Roberts' attorney Jeffrey P. Minear filed a document in Newdow's lawsuit saying that Obama wants the words "so help me God" included in his oath of office.
The Justice Department and attorneys general from all 50 states have filed motions at the federal court asking for the lawsuit to be thrown out.
The oath dictated by the Constitution is 35 words long and reads: "I do solemnly swear (or affirm) that I will faithfully execute the office of president of the United States, and will to the best of my ability, preserve, protect and defend the Constitution of the United States."
The National Archives says that George Washington added the words "so help me God" when he took the oath at his 1789 inaugural, and most presidents have used it since. However, some have argued that the first eyewitness account of a president using those words came at President Chester Arthur's inauguration in 1881.
Named in Newdow's lawsuit are Roberts; Sen. Dianne Feinstein, D-Calif.; and the two pastors invited to the event, the Rev. Rick Warren and the Rev. Joseph Lowery.
U.S. District Judge Reggie B. Walton will hear arguments on Thursday.