What's that Smell?

Cleaning checks came and went about a week ago. However, the night before Rebecca and I walked into our apartment to a disturbing odor that neither of us could place. Was it the trash? No. The bathroom? No. After going to get a drink of water I realized that the smell was indeed coming from some of our kitchen rags. And it was bad. It was really bad. So after a short discussion, Rebecca grabbed the bag and placed it outside, hoping that the smell would somehow disappear.
The next day she took them to the laundry room to be washed. When they were finished she left them in the washer with the lid up, to air them out. When she came back later that night she found a putrid odor wafting from the washer. After another discussion (one that was not so short) she ran them again, with better detergent. Joanna then threw them in the dryer right away. Later that night I retrieved them from the dryer. Any better? No. As soon as I opened the door to the dryer I could smell them. It was pretty bad. So I stuffed them into a bag and we stuffed the bag into a closet. After realizing that all our coats were going to be smelly, we took the bag out and placed it into the kitchen.
Tonight Joanna spilled spaghetti sauce on the counter: my worst nightmare. As we do not have paper towels we both knew that it meant that we'd have to use one of the rancid rags to wipe off the counter. I lifted up the bag and wanted to throw up. Joanna was like, "do they smell?". After I said yes, she smelled the bag for herself and decided that on the whole, they did not smell. Then she grabbed an individual rag to wipe off the counter, smelt it, and gagged. Then proceeded to wipe off the counter.
I fear for the sanitization of our kitchen due to these rags. But we're also at a loss as to how many times we'd have to wash them before the smell goes away. And we're a little unwilling to keep wasting our quarters on the issue.