what about simmering some white vinegar and baking soda in it....seems like that should help...

Is it possible the oil used to coat it has gone rancid? Maybe it wasn't baked in (heated up) enough.

Bake it for a number of hours a little cooler than it takes for it to smoke. Use newspaper or brown paper sack to mop the pooled grease out of it periodically (be very, very careful with your hands, arms, and paper when you do this). You may need more than one session of this; you really want to bake out as much of the grease as you can. You can scrub it with salt (and paper) each session when it's only slightly warm, which should help a little. Once you've gotten as much of the stuff off it as you can, reseason it.

If you live in a hot sunny place, in between sessions you can put it out in the sun (set it on a lot of newspaper to protect whatever it's sitting on) for some more low-tech treatment.

The problem with washing these pans when they're oily (and I'm assuming it is if the pan is properly seasoned) is that you can sometimes make a soap-oil emulsion that stays on the pan and is wicked hard to get rid of without a lot of exposure to heat.

It is hard to say how sensitive your nose is... but cast iron has a mineral scent of its own. The seasoning oil may be rancid so it is best to ensure that is not the case. However, I really believe there is a scent and subtle flavor when using cast iron. I have well seasoned but rarely used cast iron skillets and a dutch oven. I find them a PITA to use because modern dish detergents strip the seasoning and cause rust. In the day I was taught that once seasoned these pans should not actually be washed but wiped with paper towels or a damp dish cloth to remove food traces and immediately dried. Old enough to remember cast iron was the original non-stick surface.

Just get a new one. They're $20.

I never use soap when I wash my cast-iron skillets, and I dry them on a stove top burner on high heat until the remaining water droplets sizzle. Soap (even gently eco-friendly dish soap) strips the seasoning pretty quickly. Maybe you need to wash it hard in a good dish soap -- even Brillo, maybe -- then rinse it very thoroughly and then re-season it?

P.S. I've never used the oven method of seasoning. I use the stove top. Put a thin layer of a good oil in the bottom of the skillet and keep it on a burner at the lowest possible heat for several hours. As the oil dissipates/sinks in, add a little more, just to keep the surface of the skillet covered. After a while -- at least a couple of hours -- turn off the heat. Once it's cooled, sop up left-over oil with paper towels.

The oven method sounds a lot quicker!

If you have a self-cleaning oven, you can run a cleaning cycle with the pan in it. That burns off the existing seasoning. Then use grapeseed oil (high smoke point) to season as per manufacturer's instructions. Trader Joe's sells it.

And (as you probably already know) there are specific regimens to follow for cleaning, scouring and drying, especially the "don'ts", and most especially no [toxic] dishwasher detergent, which will get into the pores.

But in the end it's all worth it.

That's happened to me. Just strip it and reseason it and you'll be passing it on to your grandchildren.

That plastic smell sounds like rancid lard or crisco to me...if you have a clean cycle I would use it (after removing all flammable/ meltable parts) or submerge in it the white ash of a camp fire(preferred). Failing that use steel wool with a paste of dish soap and baking soda to remove the seasoning. The pan probably didn't get used for a long time and went rancid. If it still smells allow your pan to sit in water...it will rust and the season will come off. remove the rust with the steel wool. Baste with solid cooking fat or olive oil and submerge in white hot campfire ash or in a 400 degree or higher oven (and a cookie sheet below to catch grease drips) for about 40 minutes. Wipe with rag or paper towel to remove excess oil. Use regularly,lightly oil and avoid dish soap to avoid having to do all this work again . I have had mine for 15 years and it still works jim dandy. My aunt is still using my great grandma's set and it's been in use for 80 plus years and still works great...actually better than mine because it has more season.