Do I need pull-down resistor on Enable pin cd74hc4051
Can I directly connect enable pin to ground? I am not going to use it. 


Yes, generally it is good practise to tie all unused inputs of digital devices to eiter GND or positive supply voltage.


  Also can I connect all unused pins of LM324 op-amp to ground through single resistor?


You can, but that would waste power; instead tie the negative input of each unused opamp to its output (which forms a voltage follower) and the positive inputs of all unused opamps to halfway between positive and negative supply voltages, using a resistor divider (or GND in the case of split supplies). E.g. like this (shown for a single opamp):



For more details about opamp termination, see Properly terminating an unused op amp and What shall we do with the unused opamp .