Here's 3 shots of my wheel well after being thoroughly washed with a stiff brush.
Any dirt clods have been removed.  There was actually a dirt clod that I thought was a blob of bondo since it had been painted over!

The rough stuff is undercoating.  I don't know if that is from the factory or put on later.
Either way, it's nasty stuff to get off.  I did try goop (hand cleaner stuff), which did nothing but make a mess.

I discovered a product called "Peel Away" after removing three layers of linoleum flooring in the kitchen of my previous house (which I now rent out).  The final layer of flooring was tar paper glued to hard wood flooring.  I spent many hours doing tests with various nasty chemicals and found "Peel Away 7" to be far superior to anything else on the market.  Best of all, unlike toxic strippers, the smell is actually tolerable.  I wouldn't go making an air freshener out of it, but you certainly won't pass out or get light headed from it either.  Don't let that fool you though, you must wear a good pair of rubber gloves when working with this stuff.  Get it on your skin and it's like getting a burn.  One container, which is less than a gallon, costs about $60.  I'd estimate that you should be able to do 2 entire auto underbodies with one container.  I've also previously tested, and found it to do a superior job on that nasty black windshield adhesive.  This product is not advertised for this use, but it sure beats anything I've seen to date.  It's marketed primarily for use as a paint remover for fine furniture and household moldings.  Do not confuse this product with "Peel Away 1", which does have toxic fumes and is substantially cheaper and less effective.

My previous tests have shown that It doesn't work very well as an automotive paint remover, which is fine by me since I'm really only interested in removing the undercoating.  I spread it on with an old large paint brush that I will dispose of later.  It has the same consistency as mayonnaise.  I put it on thick and only on the areas that have undercoating on them.

Though it's tempting to just start immediately scraping, since you can see it's having an effect by the color change from white to tan, you need to leave it on at least 12 hr.. preferably 24.  It needs time to eat through to the bottom of the undercoating.

To prevent it from drying out while it's doing its thing, you have to cover it with their special paper, which is like a cross between thick tissue paper and wax paper.
You want to cover it carefully.  The idea is to have a consistent layer of "Peel Away" under the paper.

Above is what it looked like right after I finished.
Below is what it looked like 18 hr.. later.

Using a 1" flexible putty knife, I scrape the "Peel Away" off onto the overlaid paper.
There's no real effort involved.  It all comes off easily and is now like black clumpy mayonnaise.
It's a messy job, but simple and you can breath!

After all the "Peel Away" is removed, wash it down with water.  Note that the original paint is still there.
In fact, the white splotch in the center is probably from the original outer paint job since this car was originally white.
After washing it down, any bare metal surfaces instantly develop flash rust.
No big deal since I'm going to Por-15 it anyway and I'm going to wire brush the remaining paint off.

The "Peel Away" has obviously had an affect on the remaining paint, since it wire brushes off instantly.
It didn't take any more than 15 minutes to get all the paint off with the wire brush drill attachment.  I used the typical "cup" kind of wire brush.

OK, so I am missing a few pictures of the Por-15 process, but from here, I followed the directions that came with it.
1. Clean with Por-15 degreaser and rinse with water (flash rust redevelops).
2. Treat with Por-15 Metal Prep and rinse with water (Metal turns cool orange and blue colors)
3. Dry thoroughly (I let it sit overnight)
4. Two coats of Por-15 (allowing first coat to dry as instructed before applying the second)
5. Finish Coat with Por-15 Chassis Coat Black (allowing Por-15 to completely dry - overnight)
 

I couldn't resist doing the brake drums after I saw the final result.
I didn't bother putting Chassis Coat Top Coat on the drums.