If one wakes up during the time of Asr, should the Dhuhr prayer be observed first, or Asr? And if one wakes up during the time of Maghrib, should the Dhuhr and Asr prayers be observed first, or Maghrib?

Whoever wakes up during the Asr time and has the Dhuhr prayer due, must pray Dhuhr before Asr, because the ordering of the two present prayers is obligatory and a condition for the validity of the second prayer. This is indicated by the action of the Prophet (peace be upon him) on the day of the Battle of the Trench, when he prayed Asr after sunset and then prayed Maghrib afterwards. This applies to someone who slept through Dhuhr and Asr until the time for Maghrib arrived.