For your consideration ...
I would bet that you have an exhaust leak somewhere, that when under acceleration, which creates higher exhaust pressures and concentrated exhaust gasses, finds a weak point somewhere in the exhaust system and escapes. Which, by smelling it after and during acceleration, would most likely place that leak in the engine compartment area since you are moving forward and any exhaust leak post engine compartment wouldn't be detectable. Those gases you're smell are permeating, (and possibly through the A/C duct work firewall pass through), somewhere through your firewall area. So, pop the hood and inspect for exhaust leaks at idle and as well as revving up the engine a bit to higher RPMs to see if you can locate a leak.
Also, with upstream and downstream oxygen sensors, pre and post catalytic converter, if there were a converter blockage, you would be throwing a code and seeing a "Service Engine Soon" light on the dash.
Good luck and please report back if your find anything.