First of all,

What you are describing certainly qualifies as a crisis.
Water alone will do a decent job on your clothes and dishes. Don't sweat the lack of detergent right now. As for food, are there any emergency food banks you can visit? I know of some private ones in our area that you don't have to go through much if any screening to use. They are open to anyone and serve a lot of families like yours who don't qualify for assistance but are in a food emergency.
Can you catch a ride to work with anyone? You could even fib a little and say your car isn't starting if you are embarrassed about your lack of gas money. Just make sure you don't ride with someone who is going to expect gas money from you.
Do any of your friends or family know that you are out of the basic necessities for a month? Are you willing to tell people that you are experiencing a financial crisis (at least a short term one, nevermind about the back taxes and hospital bills) Many a time I have invited over a friend's family to eat with us because I knew they were struggling with putting food on the table. I would certainly open my pantry to a friend who needed toilet paper, soap, and other basic items. Sure we are struggling too but that is what it means to have community.
Also, the local domestic violence agency here receives WAY more donations of household items than they could ever use for just for their clients. You know all of those folks who save hotel soap, bottles of clearence shampoo and things like that to donate to the women's shelter? They pretty much have an open door policy to give away that kind of thing to families in crisis without any screening process. My dh used to work at the agency, and then a few years later when he got laid off from his current job they called me up with an "errand" they wanted me to run, and when I stopped in they gave me a humungous bag of soap, shampoo, diapers, toilet paper, razors, laundry soap, pads, you name it. It barely fit in my car. It was very helpful.
Does your community have a crisis hotline? My dh used to work at the crisis line and people in your kind of situation (out of food, out of basic needs with several days or more till payday) called a lot. He was able to connect them with resources to help.
Take care, mama. I hope this helps.
Edited for being repetitive and redundant
