Four Half Bridge Load Sensors outputs highly fluctuating values
+/-200 counts means you have &lt; 8-bit noise.

You say your ADC has 20-bit resolution so if you are using the full range of the input then the most significant 12 bits will be stable and your noise level is less than 1 / 2¹² = 1/4096 = 0.025% (if my calculations are correct).

I have no idea how to make a circuit or amplifier quiet enough to prevent noise on the least significant eight bits of a 20-bit ADC!