Hi,
Divide the problem/questions in two parts:
The ADC and it's specifications ... and your application with your requirements.
The ADC:
I used the differential mode of AVR's ADCs.
--> All I can say: They work as described/specified in the datasheet.
The ADC does not care if the signal input is a strain gauge or any other source. It mainly depends on voltage, current, impedance.
Your application/requirements:
You need to decide the requirements first (with values, units, tolerances), then you can compare them with the specifications of the ADC. This will show whether the ADC is suitable for your application or not.
--> For some strain gauge application the ADC may be suitable, for other strain gauge applications not.
***
Side note to the "24Bit" resolution:
There is noise, there is temperature drift, there is drift with time, there are unlinearities and even more errors...all in the strain gauge, ADC, amplifiers, resistors, voltage reference...).
In most strain gauge applications I have seen the overall performance was less than 9 bits. In some advanced professional designs one maybe get to 12...14 bits (12 bits means 0.025%). 24bits is definitely out of reach.
(I see the "24 bits" just as a marketing value, they are not useful)
Klaus