To get the circuit clean divides into several different steps. Two of them are mentioned here:

1. Try to minimize ground currents on common ground plane.

Try to imagine how the many and different ground currents are flowing, when the transistor is switching and as consequence the 4049 inverters.
One sort of ground currents can easily be decreased by using decoupling capacitors at those points, where components draw sudden supply currents: If there's a suited decoupling capacitance, then a certain portion of the sudden supply current will flow through the decoupling capacitor instead of running across the whole board. If you additionally add some series impedance to the decoupling capacitor forming a low pass filter, then ground return currents running across the whole board can even more drastically be reduced.
What sort of filter is adequate can only be stated, when more information about your application is given...

2. Insert filters in signal path if needed.

You told, that noisy output of OPamp is fed to some comparator. If the signal is noisy at input of comparator and power supply measures couldn't remove the noise, then you could also add some signal filtering at input of comparator. A simple low pass filter can help a lot.
What sort of filter is adequate can only be stated, when more information about your application is given...

By the way, why not using MC14504 level shifter?

Kai