Yeah, I faced this once while renovating my only bathroom. I accidently broke the back of the toilet and found myself without facilities for a while - until I could repair rotted flooring and get a plumber in to install a new flange.
The good news is that you've still (hopefully) got clean running water.
I got to know the local McDonalds restroom all too well. The only in-home alternatives I can think of is to use kitchen garbage bags (lots of them) and sit on a 5 gallon bucket. Some places sell seats that fit on top of them - I've thought about getting one for "emergencies". Do you have any close friends who would lone you an RV with an on-board toilet?
For body cleaning, my advice is to get used to sponge baths - they can get you pretty clean - better than nothing. The worst of that for me was hair washing. We ended up using warm water to wash hair and then rinsed using the COLD water from the garden hose outside. Hint: If I were building a hose - or at least replumbing it - I'd put valves in that would allow me to run a mix of warm & cold water out through the hose. That way I could fashion an outdoor shower of some kind - plus it would provide warm water for washing dogs.
For dishwashing, go camping in your home: Use the three bucket method that Scouts use - 1. Wash in warm soapy water, 2. Rinse in warm water, 3. Sanitize in luke warm bleach water (using min. 1.5 teaspoons bleach/gallon water), 4. Air dry. When done with the water, dump it somewhere that is least impacting to plants/animals. Another alternative is to use you kitchen sink as normal but remove the trap and put a 5 gallon bucket under the sink. Don't forget to empty it promply!