4-bit counters not working properly
Summary: Seeing those photos, there are several concerns (including the decoupling capacitors' location, type &amp; value, and the lack of connections to 74HC161 inputs A-D). Making the circuit work reliably might be an iterative process for you.
However, the first and clearest problem is: You have connected the oscillator wrongly. You need to swap your connections to pins 8 &amp; 14 on the oscillator.

Details:
Looking at the package drawing from the datasheet for your MXO45 oscillator, with my annotations in red:

For the MXO45 &quot;DIP-14&quot; version you have, it has 4 pins actually present in DIP pin positions 1, 7, 8, 14.
Its pinout is:

So in text form for the &quot;DIP-14&quot; version:




Pin
Symbol
Function




1
EOH
Enable (not used on MXO45 version)


7
GND
Ground


8
Output
RF Output


14
Vcc
Supply Voltage




But you have connected:




Pin
Symbol
Connection




1
EOH
Supply Voltage (not used on MXO45 version)


7
GND
Ground = OK


8
Output
Supply Voltage = NOT OK


14
Vcc
Output to 74HC161 = NOT OK




We can see those incorrect connections, in the photo of the oscillator on the breadboard you kindly added:

So your 74HC161 counters are not getting a clock signal, because they are connected to the power pin on the oscillator to which 5 V should be supplied.
Connecting an oscillator's output pin to the 5 V supply, might have permanently damaged it (I don't see a claim in the datasheet that the oscillator will survive a shorted output pin). Since you said that you have tried several oscillators, then you might have damaged them all.
If the oscillators you have are still undamaged then, as a starting point, swap the connections to oscillator pins 8 &amp; 14, so that the 74HC161 counters are connected to the oscillator output on &quot;pin 8&quot; and supply 5 V Vcc to the oscillator on &quot;pin 14&quot;.
I would also disconnect pin 1 of the oscillator, as your MXO45 version does not support the output enable function (see page 1 of the datasheet) - the MXO45T or MXO45HST 8-pin versions do support that functionality.