From the kickstarter page:
We'll have more exact figures soon but:
Full transmit: Up to ~220ma at max range/data transfer (but more like 115ma in normal use while sending/receiving data)
Running but not actively transmitting: About 15-50ma depending on load.
Running with WiFi off: about 15ma depending on load.
Sleep: (CPU suspended) About 1ma
Deep sleep: About 50-70ua
To achieve the last two you'll need to disable the power LED jumper.
9v batteries are not the best source of power for this sort of board unless you can get into the lower power modes for very long periods of time. Energizer state approximately 400-500mah at the typical load for the Oak. So at 'typical' loading, you'd be getting around 4.5 hours at best on a new battery. I would be much better to use a 6xAA pack... with NiMH or alkaline cells. You'd be looking at 2000-2500mah of capacity then. Or perhaps a pair of 18650 lithium cells with a protection circuit so they don't get over-discharged.
Regardless of that, to get more than say 4-5 days runtime on batteries without a massive bank of batteries, documentation on how to access the lower power states is needed. Even just turning the WiFi off for 50 seconds would amount to a significant improvement in runtime. With your unit in mind ... I can't see why it could't get down to the deep sleep state for about 55 seconds, and then power up, grab the new sensor data, transmit it, and then go back to sleep. And if this is anything like the deep sleep from NodeMCU... it is dead easy when programming, as to wake up from deep sleep, the MCU is rebooted - so your code runs from start to finish every time. In that situation... you be looking at getting several days use from a 9v battery easy.