Oh really? That's not the in the oaths I've read.
http://www.history.army.mil/html/faq/oaths.html
Enlisted are sworn to obey the orders of the President, the officers appointed over them. In additional, they are sworn to support and defend the constitution.
Officer oaths are simpler; they are the ones with the leeway to disobey orders. Their only obligation is to the constitution.
The constitution firmly establishes the power of the President and Congress to control the military. It is constitutional for Congress to regulate the military as they see fit. The only way around this is if the order itself violated some other part of the constitution. I haven’t heard a good argument yet for the repeal of DADT being unconstitutional, therefore I don’t see how any military member can be true to their oaths and disobey.