I have 2 year lease agreement for renting a house from 8/21/09~8/21/11.
House was foreclose and sold at auction on 5/24/10.
The new landlord is asking me to move out by 8/31/10, but asking me to pay the rent for month of August, but forgiving the rents for month of June & July.
But, they will not offer me the deposit (which I gave to my OLD Landlord), or the moving cost. Because of forgiving the rents for month of June & July.
Does is sound resonable or should I ask for deposit & moving cost?

It sounds like the landlord is offering you a fair deal. Your lease was terminated by the foreclosure so they shouldn't have to pay you for moving costs. Normally they would not be responsible for returning your deposit since it wasn't transferred to them by the old landlord. In a normal situation you would lose the deposit. Since they're not charging you for June and July they are basically reimbursing you for the deposit you lost, which they don't have to do.

https://www.askmehelpdesk.com/real-estate-law/do-have-pay-rent-new-landlord-497026.html

This is your third thread about the same issue.

Please ask your question only once, than wait. Sometimes it can take a while for the right expert to see your thread. Please be patient as we all volunteer here and cannot be on the site 24/7.

Thank you.