Earlier quoted context omitted.
Even atheists must do the part with God?
As far as I know, it may usually (always?) be omitted. Oddly enough, it didn't require a Supreme Court decision, because the precedent was set with the first such oath: the Judiciary Act of 1789 was the first to specify a legal oath ending with "so help me God", and it at the same time explicitly included an opt-out clause, after which that has been accepted practice. See Sec. 7 here: http://memory.loc.gov/cgi-bin/am…
Edit: The reason I say that phrase doesn't make any sense is because "God" has so many inconsistent, incoherent definitions that it seems nonsensical to request help from it. No idea what "God" even is.