Well...I'm right in the middle of the same thing on my 74 Duster...what a pita...I pulled the k member so at least I can stand in the engine compartment. So far I have used Dawn dish soap and a stiff bristled brush, easy off oven cleaner, scotch brite, a DA and an angle grinder with a scotch brute pad. I am still not done...maybe today...

My preferred method is chemical stripper followed by sandblasting. Cover the painted surfaces. Use the thick solvent based "aircraft" stripper found at some of the big box stores. Its good stuff! A gallon should do the engine compartment. Paint it on a small area with a cheap paint brush. Let it sit for a half hour or so, then scrape the surface with a razor blade scraper, changing the blade as needed. Wire bristle "tooth brushes" also work well. I use a large shallow cardboard box and allow the scrapings to fall into the box to minimize cleanup. Plastic sheets on the ground will also work.

I then sandblast the areas that are rusty or still show paint. I use a cheap suction feed unit. My air compressor isn't all that big. Blasting it all would take too much time and leave me with a beach afterward. The majority of the surface comes clean with the stripper, the blaster cleans up the other areas.

Prime with what you like afterward.

Making a mess is part of the fun. A little planing upfront will minimize the cleanup. Best of all its super low buck but you will have some time invested.

Spill a few bottles of brake fluid on it.. that will strip it real quick.

On my 70 Cuda, I have stripped the interior and underneath the car with an electric angle grinder and wire discs. A cheap wire disc (about $4 each) will very quickly strip about 10 square feet of car down to the metal. Last weekend I completely stripped the interior (roof, floor, firewall, rear) in less than 3-4 hours. I then wipe everything down with acetone and usually use etching primer. Corners may require chemicals or a dremil tool with wire brushes or some selective minimal sandblasting.

The photo here shows about 20 minutes of work in a wheel well. You can see the wire wheel went through dirt, undercoating, paint and primer like butter.

I prefer this method because its cheap and fairly quiet. HOWEVER, you must protect yourself because those cheap wire discs will fling metal spikes as they wear and they will penetrate skin so cover your eyes with good goggles and protect all other skin with thick clothes. Also, if you are in a confined space, keep a fan on you or wear a respirator since you don't want to inhale any of that crap.

Here is a link to the knotted wire discs I was talking about. I also have plenty of photos of my interior all stripped down from last weekend.

http://www.amazon.com/gp/product/B00B21CH7A/ref=oh_aui_detailpage_o02_s00?ie=UTF8&psc=1

Here is a photo of the interior work I did this weekend. The wheel also does a number on rust.

i keep coming back to this thread and I am amazed at how much work you guys do to strip paint. 1 hour of blasting and your ready to epoxy. the amount of time spent plus discs / caustic strippers / sandpaper ect is about the same cost as a guy like me coming and blasting. no warpage, damage or trapped media. its clean and the rust is gone

crazy amount of effort for such a easy job.

I like the idea of blasting I've seen excellent results from it.
I can't speak for the rest but my time is FREE when it comes to my cars...
It's countless hours I'm in the garage and the kitchen witch is in the house...

Cheap = the roloc discs and/or the 3M wheels. I've done the wire wheel and it's good for 10 minutes, then the wires lay over, slowing the process and they start shedding. This is how I've done the last 2 compartments.
Faster = blasting, but you gotta really work to get all the stuff out before prime/paint. This is what I just had done to my entire van body.

Stripper is something I don't have a problem with on large surfaces, but an engine compartment has too many crevices and pinch welds. They will hold the nasty in and can bleed it out after paint. I did this on a car many years back, but did not use it in the jambs and other seamed/welded areas.