Do all federal judges need to take an oath of office?

Yes. US Supreme Court Justices must take two oaths of office: the first, a Constitutional Oath, is required of all federal employees except the President; the second, a Judicial Oath, is unique to the federal judiciary.

Explanation

US Supreme Court justices take two oaths of office. The first, a Constitutional Oath mandated by Article VI of the Constitution and 5 USC § 3331 (federal law), is sworn by all federal employees except the President:

"I, _________, do solemnly swear (or affirm) that I will support and defend the Constitution of the United States against all enemies, foreign and domestic; that I will bear true faith and allegiance to the same; that I take this obligation freely, without any mental reservation or purpose of evasion; and that I will well and faithfully discharge the duties of the office on which I am about to enter. So help me God."

The second, the Judicial Oath of Office, originated with the Judiciary Act of 1789 and continues as a requirement under 28 USC § 453, but was amended slightly in 1990:

"I, _________, do solemnly swear (or affirm) that I will administer justice without respect to persons, and do equal right to the poor and to the rich, and that I will faithfully and impartially discharge and perform all the duties incumbent upon me as _________ under the Constitution and laws of the United States. So help me God."

The original text "according to the best of my abilities and understanding, agreeably to the Constitution" was replaced with the less ambiguous "under the Constitution."

On occasion, the Constitution and Judicial Oaths are combined and taken at the same time.

Article VI, Section 3

"The Senators and Representatives before mentioned, and the Members of the several State Legislatures, and all executive and judicial Officers, both of the United States and of the several States, shall be bound by Oath or Affirmation, to support this Constitution; but no religious Test shall ever be required as a Qualification to any Office or public Trust under the United States."