Solubility of oxygen in water is dependent on the temperature and its partial pressure. On the other hand, ammonia forms hydrogen bonds with water molecules, that is, the nitrogen on ammonia and oxygen in water each forms a bond with the hydrogen of the opposite molecule. This hydrogen bond causes dissolution of ammonia in water. The huge difference in solubility of oxygen and ammonia in water is because in addition to partial pressure and temperature dependence, ammonia forms hydrogen bonds with water molecules
QUESTION:
That's the key: the high degree of hydrogen bonding.
By the way, what is the solubility of ammonia in water compared to the solubility of oxygen in water?