Assuming you are an active player you play an Oracle of Mul Daya or Crucible of Worlds. Could you play your land before they kill Oracle of Mul Daya? Would you be able to play lands off of Crucible of Worlds if they would try to destroy it?
APNAP doesn't factor in. APNAP is used when multiple players need to make choices simultaneously, and when stacking triggered abilities of multiple players. These questions are strictly about priority.
As the active player, you get priority after a spell resolves.
If you were to play a land then (a special action), you would get priority again.
So the answers to both questions are yes.
It works the exact same way as the planeswalker case, Mentioned in your other question
Once Oracle resolves, assuming that it's your turn, you have priority, and you have all day to take whatever actions are legal to you, until you pass priority. This includes playing your second land for turn(which doesn't use the stack anyway), and you'll still have priority after that.
For instance, if you were to play Fastbond, you could play any number of lands, without your opponent receiving priority, assuming that no triggers are being put onto the stack.