I am not familiar with the Teensy boards, but looking at your breadboard picture makes me wonder: Are you shortcutting Pin12 + Vbat + 3.3V ? And also Reset + pin13 ?
Your sensor is this, http://www.omron.com/ecb/products/sensor/21/2smpp-02.html
For accurate pressure measurements, it should should be powered with a constant current of 100uA.
You use it with 5V and I think the connections in your breadboard drawing are okay. It should work, but you won't get the accuracy it is designed for.
The datasheet show how to use a opamp as current source.
Sensor seems to be 4x20k serial/parallel (I'm not sure), and with 100uA, the sensor needs about 2V (but I'm not sure).
With 2V, the outputs should be around 1V with a little offset.
In the datasheet the absolute maxium for the supply current is 130uA. With 5V you might have damaged the sensor already.
If you remove the INA122 and use a potmeter for the analog input, are the readings normal ?
Could you measure the sensor output with a multimeter to see if that is normal ?