Conclusion
I'm not sure about this. While the clothes were washing I reached in and felt the water and it wasn't "slippery" like when regular detergent is in. There were absolutely NO suds at all in the water. My first impression was:
1. It doesn't do ANYTHING
2. The water wasn't warm enough to activate it.
#2 sounds plausible because the water from the cold tap was warm enough so that the machine didn't need to turn on the hot tap. I confirmed this by shutting off the cold tap and the water stopped coming in altogether. Then selecting "hot" water for the wash temp, the hot water starting coming in. Apparently the Kenmore Oasis has a very cool "warm" setting. So now I'm going to do a load of towels on HOT water to see if the Oxiclean does anything.
So far, as it stands, It's a dud, but it might change my mind with the towels.