Can i write off my 2nd home?

if the home is paid off, the only deductible item would be real estate taxes paid.   if you could be more specific about what you mean, maybe a different answer would be in order.   you can not just expense the second hone because there is no mortgage 

house was sold at auction by the local government due to RE tax being in arrears. No mortgage on the property

No, you can't take a loss on personal use property.