I am renting a USDA home that was not supposed to be rented. Now the landlord wants to sell it. Can I sue for back rent money?

Unfortunately, that is between USDA and the owner. Not an attorney but I say no. I would consult a real estate attorney though.

Since this is an issue between USDA and the homeowner as a mortgage consultant whether you could received back rent money by suing your landlord would never come into our area of expertise. You definitely need to consult with an attorney if you wish to proceed with something like that. It seems the USDA could be entitled to the rent money.