According to the Oakland International Airport's FAQ:
May I remain overnight in the terminals?
Connecting passengers with an overnight layover may remain overnight in the terminals pre-security only. Since we are open 24 hours a day, 7 days a week, law enforcement officers are always on site and you may be asked to show your identification and proof of travel.
If you decide to you want a little more comfort than an airport can provide, and want to stay in a near-by hotel rather than remaining in the terminals, Oakland International Airport suggests you stay at one that has a complimentary airport shuttle available in the early morning hours. The closest hotels are on either Airport Access Road or Hegenberger Road, or read "Airport Area". You may find the list of area hotels on our website at: visitoakland.org