This is an important topic with disasterous consequences if the incorrect methods are employed so I'm going to do something that I don't often do and that's say, "This is dangerously wrong", for some things that have been suggested or asked about. Please don't take it personally since we're all trying to find methods to improvise or prelocate water treatment capabilities.
Alcohol is useless for sterilizing water. It does not cause water to evaporate, but the addition of water will destroy alcohol's topical antiseptic properties.
While essential for an water treatment approach in an urban/industrial setting Granular Activated Charcoal will not remove all the toxic materials that could reasonably be expected to be in NOLA flood water. It will not remove metals. It works well for volatile organics, but the charcoal will only absorb a finite amount of the volatile contaminants. If there is enough charcoal it will absorb enough contaminant to make the water potable. If there is too much contaminant the charcoal will absorb what it can and reduce the contaminant concentration by only that amount allowing the remainder through to your tea pot. If used over and over again the charcoal will eventually become exhausted. Should contaminant levels be high it will happen sooner than later.
Distilation is good if you don't have chemically contaminated water, but it will not remove all chemical contaminants either. Volatile chemicals will evaporate before/with the water and be collected in your condenser. If you were very lucky and very knowledgable you could fractionally distil your contaminated water and drive off much of the volatile chemical fraction and then condense the water.
Agitation and multiple pours through cloth filters can reduce the volatile fraction in contaminated water, but serial AC filtration or distilation is about the only way that you can be sure to remove solvents, pesticides, and gasoline components if you have urban/industrial surface water.
As a survival technique you could locate a gas station groundwater treatment unit that uses GAC canisters and rob them from the unit. As long as the GAC was relatively fresh you could pour settled water through it and have a large volume of GAC to absorb contaminants.
The katadyn tablets are expensive, but much better than any portable chemical water treatment for biologicals out there. Mechanical micro filters certified against crypto and giardia are also good. Anything that doesn't certify against bacteria, crypto and giardia is putting yourself at risk.
