The sensitivity and range of the oxygen sensors is such that they are used only in an OFF/ON sequence. At idle the engine ECU continuously modulates the A/F mixture slightly above to slightly below the target, the ideal A/F mixture from the standpoint of minimizing emissions deemed harmful to the environment. So at idle the exhaust flow alternates between absolutely NO oxygen content and the base minimum. In short the output of the oxygen sensor, ideally, will vary up and down continuously as a function, and in sync with, the modulation of the intake A/F mixture.
There are actually two parts, components, to the MAF "module", the mass airflow sensor and the IAT, the intake air temperature sensor. Colder air is denser air and at low intake flow volumes, near idle, the IAT plays a bigger part in the computation. Not to say, by any means, that it isn't always a part of the computation.
As you open the throttle initally above idle, and then more and more, provided the engine is under load, the A/F mixture will begin to move away from the ideal A/F mixture insofar as emissions are concerned, and into the region of higher, richer, A/F mixture ratios wherein the oxygen sensor becomes totally and completely useless. The engine is now operating "off-the-curve" of the oxygen sensors sensing capability.
It is in these conditions that the MAF/IAT module signals come into play for controlling the optimum level of fuel to mix with the intake airflow volume. As a trial I have inserted resistors in the IAT circuit, series and parallel (at different times) to modify the intake sensed temperature above and below the actual intake temperature, ~72 actual to 92F "sensed", and 72F actual down to 45F. False sensed voltages were verified via AutoTap's OBD-II scanner/reader.
There was never an indication that the engine ECU "knew" or detected the flawed intake temperature signals apparently accepting them as "true" readings.
The test runs, typcally over 400 miles of highway driving at a reasonably constant ~70MPH, of the vehicle in question, a 2001 AWD RX300, resulted in no meaureable difference in average MPG with the intake temperature falsified above, below or with actual sensing.
But I fully believe that had I tested on a dyno the available engine HP output would have changed in the range of +/- 10% or more. So the IAT false "cold" modification that resulted in an even richer mixture than the factory default target would have undoubtedly shown itself at track time.
The on/off your referred to regarding the O2 sensors if determined by whether you are in closed or open loop at the ECU. If your are in closed loop, the O2 sensors are never off but are increasing and decreasing in current in response to the mixture it reads. These adjustments are fed into the fuel LTFT. At idle, closed loop, the amount of fuel injected is a combination MAF, O2 sensors and LTFT. The MAF has no way of controlling the PROPER air/fuel ratio in the engine other than what has been mapped into the ECU. At WOT, if the MAF for some reason is reporting the incorrect amount of air and temperature (in cases where you have an intregrated MAF/IAT) then the incorrect reading will NOT be adjusted for by any other engine sensor.
Modifying the air temperature reported to the ECU will also effect the engine's timing and this has been a method of fooling an ECU for years. Remember, the O2 sesors are always controlling the fuel/air mixture except in open loop (near or at WOT) whether under load or not. It's a fairly efficient method of contolling the mixture.