My landlord just notified us that he had stopped making mortgage payments on his house a couple of months ago and that he is giving it to the bank. He said we are safe to stay for two more months and after that bank might kick us out. As I understood he no longer takes any responsibility for the property. In that case is it legally OK for me to stop making rental payments while I am in drastic search of new place?

If he tells you that it is OK not to pay him, then it is fine,

Legally as long as he owns it, ( and it may take 4 to 6 months) after he stops paying for them to actually foreclose. But as soon as you don't pay one month, the landlord ( who stills owns it until it is actually foreclosed) can evict you if he wants to. Now he may figure since he is not paying you don't have to pay. So if it is OK with him, great, but if he wants you to pay, he could evict you if you don't.