Ok, here's the latest. I hope all of my issues are over and I'm still not sure what was going on, but here's what I did:
1) Noticed a low spot between this house and the neighbor's house, which collected a lot of water next to the foundation. Put in a drain pipe to drain this water away from both houses. Unfortunately water continues to back up next to my neighbor's house, pouring into their crawl space when it rains. Hopefully my pipe will help their property as well.
2) Pumped out the water from the crawl space. Used a small shovel and heavy plastic bags to remove the surface black stuff from the crawl space. When it was cleaned out, spread quite a bit of 20 Mule Team Borax all over the crawl space., because I hear it kills or inhibits growth of any bad stuff.
3) Put down a high quality vapor barrier wall to wall.
4) Hired someone to dig around the foundation in the crawl space, installing drain pipe and a sump pump to remove water. Here's the kicker: While digging the drain pipe around inside of the crawl space, my hired help noticed the PVC drain waste pipe going into the cast iron sewer line was not secured properly, so he fixed it.
So, as of now, the problem seems to be fixed. I'm wondering if the black substance that appeared in the crawl space was actually oil which came from the sanitary sewer system, which backed up into the crawl space due to the jacked up plumbing pipe when we had heavy rains in the area. Wishful thinking? Thoughts?