Electronic – Meaning of “per digit” for a sensor reading

The first thing I'd look at is ripple in your voltage rail. Noisy voltages are killer with a voltage divider. A higher-quality measurement system might use a regulated constant current source to drive the RTD instead of a voltage divider. An LM317 can be used to do this - hook a resistor between the OUTPUT and ADJ terminal, and hook the RTD between ADJ and GND. The value of the resistor between output and adjust will set the current going through the RTD - use a precise resistor to be certain of the amount of current.

Otherwise, attempt to do the filtering in hardware if possible. You first have to figure out where the noise is coming from to make it effective. Determine what frequencies of noise you're seeing and then probe at the input to the gain stage, the output, and the input to the ADC. If there's noise everywhere, then it's in the source, otherwise it's being injected somewhere else. Make sure all of your IC's have bypass capacitors to start with. Then make sure that you don't have any long ground loops - make everything as direct (high current) of a connection to ground as possible. Don't daisy chain grounds - everything should get its own connection to ground that doesn't run through other chips.

If you're seeing noise at the source, chances are it's your voltage source for the divider. To combat this, you could put a capacitor in parallel with the RTD to make a simple filtering circuit. Just figure out what frequencies of noise you're seeing and match the capacitor to the resistance of the RTD and figure it out.

I'll go for the low hanging fruit here.

I suggest voltage dividers for each of the three sensors. Be sure to use stevenvh's formula for determining your other resistors for each divider: Resistor formula for voltage dividers

In short:

$$R = \sqrt{R_{min} * R_{max}}$$

The formula will help you obtain the greatest range in your Vout.

Then read your voltages with the ADCs in the AVR.