I work with a number of disaster response groups.
If you want to work with a certain faith, start with your local congregation and ask what organizations (local, regional, or national) they might affiliate with.
If you want to work in your community, contact your county Emergency Manager, Sheriff, or local Fire Chief and ask about CERT type programs.
If you want to do a specific task (chainsaw, pet rescue, ham radio) you might need to do some Internet searches to find the right groups/contacts.
The National chapter of Volunteer Organizations Active in Disaster (NVOAD)
VOAD Network is "an organization of organizations" that do this type of work and can be a good place to start. Most states have VOAD organizations to coordinate efforts, although, they are sometimes called something else.
* Chainsaws make some people and Emergency Managers nervous, so despite what experience
you know you have, some storm clean up groups are a bit cautious about new guys until
they know what type of experience you have, your work practices, risk taking, etc. *
I 'have' some volunteers now working in the Moore and Shawnee, OK area doing storm clean up (not all chainsaw) and in NYC doing Hurricane Sandy rebuilding if people are interested. It is a faith based group that does not care what your religious beliefs are, as long as you are there to help. They do not ask about the faiths of the victims, only if they need help. PM me if you would like some contact information.
Philbert