Several months back, I had the milkshake condition in the oil pan and such also. It was the oil cooler gasket/o-rings.
It does make a mess. As far as cleanup goes, this is what I did from a suggestion from some pretty sharp fellas (thanks Danno).
After replacing oil cooler gaskets, oil pan drained, replaced oil filter with a cheapie, plug back in pan, I poured about a gallon of acetone in the filler tube into the pan, then get rather creative here........I jumped up and down on the bumper, and shook the car around as much as I could, to slosh the acetone around in the bottom of the pan to get the solvent to wash that coolant off bearings, and such. Drain it out, put plug back in, and repeat above again. OF COURSE, DO NOT START THE ENGINE. Like Danno says, shake, not stir.
Now you want to add in some oil (you already put a new filter on). 6 quarts is what I put in (buy a case or so of cheapie 30 wt oil), run the engine no more than 5 minutes (at idle ONLY), then stop, drain out oil, change out filter again, put in more cheapie oil, and do again...........5 minutes, and dump it. I did this a total of three times, wasted 3 filters, and 18 quarts of oil. Put in your last and good filter, use your good oil, fill, and you should be done. You will see some milky stuff in the filler tube for a day or two, but it should go away pretty quick..........at least mine did. And I wasn't losing water anymore from the resevoir.
I didn't even worry about trying to clean the other things.
I don't remember having "thick white smoke coming out of my tail pipe". You may very well have a blown head gasket. Did you by chance notice a big drop in power/poop of the car? I would think this would also be a big indicator of head gasket problem.
Good luck!
Edit: The biggest reason for using the acetone, is, since coolant is much lighter than the oil, it helps wash, and carry it out of the pan. Draining the oil only, will leave a lot of coolant behind in the pan to just get pumped around the oiling system again. At least, thats the story I'm sticking with.
