analogRead() adding noise to signal?

Grumpy_Mike:
Looking at the circuit I think your resistor values are all out, R115 and R122 are down as 0R and R117 and R133 are down as 10M. These values are way out for correct operation.
I am willing to bet your noise is coming from the op amp not the arduino. The only filtering you have on the other amp is a feedback cap of 27pF. Why are you doing that, this is way too low to be actually effective in any sort of signal you are going to get from a pressure sensor. It is probably just stabilising the op amp because of the too high value of the 10M.
I would make the 10M resistors 220K and the 0R resistors 10K.
I would also put a 27pF cap across R116 to stabilise it. Then I think you will find your op amp will stop oscillating.

The overall layout was made so that we could swap out parts if needed, the 10 Mohm was supposed to act as an open and 0 ohm as a close and give us the capability to change if needed (such as turning the voltage buffer into some sort of filter/gain) to give us more options since this was printed on a PCB.

Krodal:
Thats what I think. Your OpAmp circuit is a noise generator and pickup for noise with that very high impedance of 10M.

Why do you use the OpAmps at all? The pressure sensor output can be connected to an analog input of the ATmega2560.
I would recommend a small resistor and capacitor for safety. You already have 680pF at the sensor output. Perhaps a resistor of 1k to the analog input of the ATmega2560, and an other 1nF to ground at the analog input.

The purpose of adding a voltage buffer between the analog input and pressure sensor was to again, give us flexibility in our design after the PCB had been printed.

We ended up fixing it by removing a 0.1 uF decoupling capacitor (not shown on the schematic) that was attached between the output of the buffer and analog input to the arduino. We had put those there because the traces we used we figured were long and susceptible to noise from the power supply. I suppose the op-amps used didn't like these capacitive loads.

Thank you for your help/suggestions.