Since your claim is that this odor seems to be at it's worst when water heater is in demand leads me to believe it is directly connected.After viewing the pictures, my opinion is that this issue may have something to do with whatever sealer that is on the vent pipe joints.Neither the furnace nor the water heater should require any type of sealant.However both should be ran out of double wall tpye B metal vent pipe(not single wall pipe). See images belowNo sealants of any kind should be required .It appears there are several places where your vent is not sealed well even with this sealant. Also around the unit are places where a small amount of surrounding air can enter the air stream such as furnace door, where furnace connects to coil, drain and refrigerant pipe openings on coil, etc .My suspicion is that as the vent pipe from water heater gets hot (as well as some heat escaping at the bad joints, this orange colored sealant may be producing the chemical odor and being drawn into the air stream.The only relation I can see about the rain is perhaps the single wall metal is cooler above ht roof line and perhaps have an effect on the amount of odor. My suggestion is next time you have the odor, go to the vent pipe and smell around the joints where the sealant is and see if it is strong there.(Of course not for a prolonged period of time, Don't want you inhaling fumes). If indeed it smells strong at that point, I suggest replacing both vents with type B double wall pipe with NO sealants. (really should be done anyway). Hope this proves to be helpful.