The Constitution is quite clear on one aspect of the oath: "no religious Test shall ever be required as a Qualification to any Office or public Trust under the United States." And yet every oath except the Presidential one -- which is explicitly detailed in the Constitution -- now ends with "So help me God."
The Constitution specifies an oath of office only for the President:
US Constitution, Article II, Section 1
"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 Library of Congress provides information on the date each President was sworn into office, as well as the location and who administered the oath. Another list contains the Bibles and scripture passages used by Presidents when taking the oath of office.
The Oaths Of Office