I'm not saying the lack of functioning downstream O2 sensors will CAUSE the misfire.
I'm saying that functioning downstream O2 sensors should be picking up the results of misfire, setting codes due to catalyst inefficiency. No functioning sensors, no catalyst codes or CEL. The title of this thread alludes to lack of codes, and no CEL being set. So I'm also wondering what else "black bear" disabled that would prevent appropriate monitoring of the engine.
What's causing the misfire has not yet been determined--but misfire + fuel in the oil sure points towards improper fuel control within the injection system. In the old days, we'd suspect a faulty engine-driven fuel pump, too. Possibly, insufficient ignition would allow raw fuel blow-by, but that would take longer. The fuel could even evaporate out of the oil and be removed via the PCV system unless the ignition misfire was REALLY bad, and the OP isn't complaining about a hard, constant misfire.
The change in the exhaust "smell" probably occurred when the catalyst quit working. Eye-burning exhaust is usually due to excess hydrocarbon (unburned fuel) in the exhaust. HC should be reduced by the catalyst. If it's not, the catalyst is cooked.
In MY driveway, there'd be a scan tool looking for misfire data. I see "fuel trim" in the graphs above, but I'm not familiar with that style of graph, and I can't make sense of it. I'm used to seeing fuel trim displayed numerically. I'd also consider a cranking compression test, cylinder leakdown test, and especially a cylinder-balance test which might also identify the misfiring cylinder(s).
