Here are the facts:
As of right now there are no evacuation orders for Military personnel and / or their families to leave Japan. As of right now any family that chooses to leave Japan will be allowed to leave with their pets.
However in some high threat level situations pets are not allowed to leave via military transport.
Those who would like to leave can do so and take their pets with them either on government chartered flights or on flights booked on their own.
Schools on military bases are still open for classes at this time.
When bringing pets on the plane you are only allowed to fly one pet per person and the pet must fit under the seat in front of you in a secure bag. Each airline has its own policy for how many pets if any are allowed in cabin on the flight. Generally these spots are given on a first come first served basis but make sure to tell the airline when you book your flight.
Pets that go under the plane in the cargo hold must be in a secure crate generally one pet per crate. You will have to book the ticket for your pet(s) in advance and might need to do so via the cargo office of your chosen airline. Check with your airline for their individual requirements.
The weather on the day of your flight cannot be bellow a certain temperature or above a certain temperature or it will not be safe for your pets to fly.
Information you will need:
Veterinarians near the American Military bases are open and available to see pets in order to issue a valid health certificate in order for them to leave the country and be allowed back in the US. Please be sure to have the documents either in English or in Japanese English so they can be read by customs and APHIS officials when you arrive in the US
There is no quarantine time for dogs or cats leaving Japan and entering the US with valid health certificates and rabies certificate. Pet birds who are originally from the US will have to spend time in quarantine. However please check with the individual state in order to make sure they don't have other requirements.
Birds that were purchased in Japan are not allowed to travel to the US at this time. http://www.aphis.usda.gov/import_export/animals/nonus_pet_bird.shtml
Pets left in Japan that must be left behind for whatever reason will not be Euthanized just because you are leaving them behind. There are shelters willing to take in your pets until other arrangements can be made to get them home to the US or you arrive back in Japan.
Important Resources:
http://www.aphis.usda.gov/import_export/animals/animal_import/animal_imports_pets.shtml
http://www.cdc.gov/animalimportation/dogs.html
http://www.usaha.org/StateAnimalHealthOfficials.pdf
http://www.aphis.usda.gov/import_export/animals/animal_import/animal_imports_states.shtml
Organizations who are willing to help:
Japan Earthquake Animal Rescue and Support - they are made up of 3 Japanese Animal shelters with facilities in the North of the country. You can post your plea for help on their Facebook page. They have now created a whole support structure via Japanese Veterinarians and other shelters and clinics willing to take in animals.
WorldVets - an organization based in the US made of up Veterinarians and other veterinary professionals that are currently in Japan helping to treat and care for animals in need. They are willing to work with families on an individual basis who are in need of help.