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.