A really bad odor started permeating the basement and we found out it was coming from the crawlspace. It turns out that there was a lot of greasy, smelly, kitchen waste water that had leaked out of the plumbing and onto the plastic vapor barrier.

The kitchen drain pipe extends straight down into the crawlspace and goes into this concrete "bowl" that is about 1 foot in diameter. The "bowl" is completely cracked on top and on it's side. Can someone please tell me what this is and what can be done to replace it?

Not sure if this info helps any but here it is anyway: The waste water pipe from the upstairs bath and toilet as well from the washing machine is located on the opposite side of the house and goes out a different drain. There is also a catch basin outside located about 3 feet away from the kitchen sink inside.

It is very possible you may have a "grease trap". This device is used in commercial kitchens.

Fix your kitchen drain first. If you indeed have a grease trap then remove it. You don't really need it in residential applications. Then, to deal with kitchen waste smell, purchase couple of bags of lime and spread it over the wet area. It will dry it out and neutralize the smell.