Legally speaking, the authority of any commissioned officer derives exclusively from the president. I don't know if the manual is still current but looking through the FM 22-100 (Army Leadership) from my era, Appendix A-2 states:
"A-2. Commissioned officers are direct representatives of the President of the United States. Commissions are legal instruments the president uses to appoint and exercise direct control over qualified people to act as his legal agents and help him carry out his duties. The Army retains this direct-agent relationship with the president through its commissioned officers."
Even if Obama is not legally President, that doesn’t necessarily defeat the legal authority of commissioned officers. Even if Barack Hussein Obama’s entire Presidency is declared void, that just means Joseph Robinette Biden has been acting President since 20 January, 2009, pursuant to Section 3 of the 20th Amendment, and that commissioned officers are his agents.