This is driving me mad! LOL I have been trying to figure out what is causing this noise for weeks. I have a video of the noise.

Here

 

So this only happens once the car is in closed loop.

Two guesses to start with, as there are no codes but please verify the CEL does "bulb check" when you turn the key to on....should come on for ~3 seconds and then go off.

EGR ports.....not just the valve but the ports in the intake manifold....could be clogged. Not a fun job on a 4th gen but can be done pretty easy.

Next, really a reach.....a lazy O2? How is the MPG on the car?

 

Agree with Poorman, possibly EGR ports clogged. Although, your video doesn't fully show the tach's rpm when the noise occurs, it sounds like a hesitation or stumble at somewhat lower rpms.

There is a Honda TSB for your car regarding an engine hesitation or stumble can be felt under light acceleration between 1,500 and 2,000 rpm due to clogged EGR ports.

Honda TSB 98-074

 

Update and better video for help in diagnosing.

 

Cool tool.

 

Cool but I cannot figure out what is causing this noise. I have clamped the sensors to the block of the engine and the transmission and no noise from them. Definite head scratcher.

 

When you say cross member....is the the one up front by the rad? Can we assume the front mount id ok?

Under hard braking....does the car seem to pull side to side.