I found the following summary of on-demand HHO system explains clearly how and why HHO gas can be used to cut down fuel consumption in vehicles.
I remind you one thing Stanley Meyer the frontier of HHO technology got murdered by TPTB years ago.
Back in the good old days, before there were computers in cars, experimenters were able to add HHO to their engines and get remarkable mileage gains and dramatic decreases in emissions. No other handling was needed to get excellent results. Similarly, diesel engines, even today get excellent results with HHO and need no other handling.
However, with the advent of the computer, fuel injection, oxygen sensors, and other sensors used to control the air/fuel ratio, a problem is introduced into this simple technology. The problem starts like this. When hydrogen is introduced, and the engine is turning more times with less gas, one of the results is that there is more oxygen coming through the exhaust. This is reported to the computer by the oxygen sensor(s) that are installed in the exhaust pipe(s). The computer reads this additional oxygen as a “lean” air/fuel mix. It then promptly adds more gas, until it “sees” the same exhaust conditions it was programmed to expect. However, it is now incorrectly adding gas when it shouldn’t.
People with modern, fuel-injected cars, who put in HHO, often report that their vehicle runs smoother, and has a dramatic increase in horsepower. But they also often report no increase in fuel mileage. This is because the computer, that was designed for inefficient combustion, is adding much more gas than is actually needed. What is needed to get all the gains available to this technology is to compensate for this additional oxygen in the exhaust.
A device was created that does just that. It’s called an EFIE, which is short for Electronic Fuel Injection Enhancer. You can find out more about this device, and how it works in the article EFIE Described. But basically this device compensates for the additional oxygen appearing in the exhaust, and allows the computer to do it’s job correctly when an HHO system is installed.