Have you checked out Team Rubicon? It's purpose-built for exactly what you're talking about. It was originally developed for returning veterans, but has expanded to include anyone. They do physical grunt work, mucking out after hurricanes and floods, cleaning up after wildfires etc.
Another good way to go is the Red Cross. If you sign up with them, you can do stuff like volunteer at disaster shelters.
One big complaint with rescue workers is that well-intentioned volunteers tend to just show up on their own, are often unprepared, and can become victims themselves, becoming a drain on rescue resources. So anyone who goes into a disaster scene needs to be totally self-sufficient, have basic survival equipment and training, and be reasonably physically fit (which is why I Mii longer do emergency services, since I'm disabled and might need services myself!)
I'd love to see an organized effort to get a fast-moving volunteer field unit together for feeding and hygiene distribution in disaster areas. We nomads know better than anyone how to deal with things like food and sanitation without running water and electricity! We could definitely contribute without causing a further burden on existing systems.
Feel free to use my brain, since it's otherwise in cold storage ;-D
Laura P. Schulman, M.D., aka...
The Dire Wolfess