Well, normally my answer to chunky paint jobs is a bath in Simple Green.
I just let it sit at undiluted strength in a sealed tub, then scrub the minis with an old toothbrush, and that's plenty.
It's basically environmentally friendly, doesn't smell like death, doubles as a regular cleaner, and doesn't generally hurt models. The worst I've experienced is staining if it's old or sometimes getting a weird texture on metal if I leave it sitting for a long time, but that doesn't really matter if you're priming the model again.
But, then there are worse kits.
I discovered Krud Kutter in a bit of desperation when the above tank showed up. If you can't tell from the pic, that isn't wet. That's glossy enamel spray paint, painted over two older paint jobs, which was packed in bubble wrap before it was fully dried, so it has flecks of plastic in it.
But, it works.
After letting it sit for a few minutes, I was able to, with some elbow grease (and gloves!), clean the tank with no damage to the plastic (I of course tested it with a bit of sprue first).
Unfortunately, I don't have a pre-primed shot, but here's the refurbished tank:
I could have done another scrub, but wanted to keep my exposure to the solvent to a minimum, partially 'cause I hate the smell of harsher chemicals. I expect that with some more persistence, I could have gotten it looking nearly new.
So, two strong recommendations, depending on how serious the job is.
Oh, and if you're pretty sure the piece hasn't been primed, an overnight soak in soapy water with occasional scrubbing can do the trick.
EDIT IN BIG RED 'CAUSE IT'S SO DAMN IMPORTANT(!)
Don't trust that something that cleans plastic well will work the same on resin! It's possible that something that strips plastic nicely will turn most model resins (i.e. those gorgeous and generally more expensive models) all gummy and horrible. Test with a bit of sprue.
In fact, that's generally a good thing to repeat. Always test on scrap before wrecking your nice models whenever using a new material, be it solvents, glue, primer, varnish, etc.