There aren't many radioactive isotopes of Oxygen and Hydrogen and the ones that there are aren't very radioactive.
As dmckee notes, there is Deuterium formed from Hydrogen capturing a neutron, this produces D2OD$_2$O, or heavy water. But Deuterium is stable and so doesn't cause radioactivity in itself. Heavy water is chemically a little toxic but not a radiation risk. You could produce Tritium when Deuterium captures another neutron, but the rates of this happening at fuel rod energies/intensities is tiny.
The most likely source of fuel pond becoming dangerously radioactive is a crack in one of the fuel rods allowing isotopes generated in the fuel to leak out.