What should I take with me as a Red Cross volunteer?

Lots of underwear and socks. A poncho liner to sleep under. A lockable bag, with some kind of lock you can use to secure the bag to something heavy. A camera to get some pics of your coworkers, etc. On shoes, I would go with comfort first. You'll be on your feet all day, but probably not doing super-adventurous stuff. A hat that shades the neck.

My first step would be to look for general world travel backpacking pack lists. They have served me well wherever I have been. If you will be moving around all day, a comfortable medium sized day pack is essential, I find it really helpful to have plenty of pockets on the outside for easy access. Specific items I have found invaluable: hand sanitizer. Leatherman Wave, needles, needle-tip tweezers, sunscreen, sunburn cream, camelback style water bladder, snacks, comfy gloves, microfiber underwear, microfiber towel, clothes for comfort over appearance, clothes you can layer, earplugs, shoes that dry quickly. Tools to document your experience: camera, journal, mini-disk recorder. And one I consider invaluable: a statement you write to yourself the night before you leave documenting why you are doing this, and what you want to accomplish, both for posterity and when the going gets tough.