It is always difficult to handle job applications after being fired. And you can't lie. Assume any potential employer will find out what really happened. Your best bet is to be completely up-front and open about why you were terminated. While the termination seems unfair the way described it, most likely your employer has a different view.
Some people decide to take any job they can get, just to get something in their work history that follows a termination. Some people volunteer when they cannot find a new job.
Without knowing all the details, it is hard to suggest ways for you to handle this, and hard to discuss any of the opportunities you may have to appeal the termination through the Merit Systems Protection Board or complain to EEO. I urge you to consult with one or more experienced employment law attorneys with whom you can discuss the details of your situation. Remember this is a public web site and anything you post here can be seen by anybody.
@MikaSpencer * * * twitter.com/MikaSpencer * * * PLEASE READ: All legal actions have time limits, called statutes of limitation. If you miss the deadline for filing your claim, you will lose the opportunity to pursue your case. Please consult with an experienced employment attorney as soon as possible to better preserve your rights. * * * Marilynn Mika Spencer provides information on Avvo as a service to the public, primarily when general information may be of assistance. Avvo is not an appropriate forum for an in-depth response or a detailed analysis. These comments are for information only and should not be considered legal advice. Legal advice must pertain to specific, detailed facts. * * * No attorney-client relationship is created based on this information exchange. * * * Marilynn Mika Spencer is licensed to practice law before all state and federal courts in California and can appear before administrative agencies throughout the country. She is eligible to represent clients in other states on a pro hac vice basis.