How can I turn ON-OFF this oscillator circuit?
Could you tell me how I can turn this circuit on and off as I did with
  the AND gate.


You could feed the enable signal into the X1 pin through a diode (eg. 1N4148) with Anode to X1 so it pulls down to ground and turns the oscillator off when low, but doesn't affect it when high.  


  The first 5 or 6 pulses can be irregular, as long as the next ones are
  at the good frequency.


Without knowing the exact requirements of your circuit I can only say that crystal oscillators take a long time to the start up, so if you try to turn the oscillator on and off directly there will be a lot more disturbance than just 5 or 6 'irregular' pulses. There could be a delay of tens or hundreds of milliseconds before the oscillator level builds up enough to clock the divider reliably.  

Since your existing circuit works, I suggest using a separate Gate IC (eg. 74LVC1GU04) for the oscillator.