All, just thought I would update this in case anyone was curious.
I did a combination of things, mostly influenced by the series "Clean your motorcycle" Parts 1-5 by DrivenandRidden on YouTube. It was a really excellent series for the type of cleaning I was doing. I highly recommend it if you have a old bike that is dirty that you want to clean up, but not repaint, resurface and all that jazz.
Basically, here's the process I used...
First, do a wash with warm water and dish soap. Try to use a toilet brush or something that will let you get in all the cracks. Don't worry about getting it perfect - this is just the initial wash. Now let it dry.
Then look around the bike, and see where the large deposits of oil and grease type stuff are (around the chain, near any oil leaks, etc). scrape these off with a popsicle stick (or something else that is soft compared to you engine). Get the largest gobs off.
Then, come back and spray your engine ( and other offending areas like the swing arm mount, front sprocket cover, rear sprocket, etc) down with some WD-40. Let it sit for 10-15 minutes. Then come back with several brushes, and scrub the hole thing down. It will not instantly become clean, but the WD-40 dissolves most stuff. Really get into the cracks and crevices with the brushes. I found a small toilet brush and a couple of tooth brushes worked great on my bike. Depending on how dirty the engine is, you may need to repeat this step. DO NOT RINSE with water.
Now get some water-soluble degreaser, like Simple Green (that's what I used). And spray down the entire engine and other bits again. Let it stand for 10-15 minutes. This will dissolve the WD-40 and associated stains. Scrub again with your brushes all over. NOW, get some water and more degreaser and clean everything with your brushes, and water and degreaser. Again, depending on how dirty the engine is, you may need to repeat this step. Be sure you get all the degreaser off... it's not too rough on your engine unless you leave it on there for long time. I did another round of dish soap and warm water.
Remember, this process will strip the oil from your chain and any other exposed bits that need lubrication. So be sure to spray your chain and grease anything else that needs it before you go for a long ride.
This did wonders for my bike. You can actually see the engine pretty well now, and though some parts need a steel brush treatment. Most came surprisingly clean. I may have to repeat the process (I seriously doubt anyone ever cleaned the engine of this SuperHawk), but this did a world of good to make the engine look great and I bet I will be able to see any leaks that are present very easily.
Also, for a more detailed explanation, I highly recommend the YouTube videos. They are really well done, with lots of good info (much better than what I have here).