The reason that you have been laid off is that there is no work. I am guessing that is not just your company, so finding a different employ may be difficult.
Are you still being paid? If so keep turning up to work. If you are being paid, you have a duty to do your duty for the company, so therefore, if your boss gives you more work, then you have an obligation to do it, and professional pride and a good reference, requires you to do it well. I think that this is the bottom line.
not having a finish date, does this matter? The company will have to give you a set notice period, this is a minimum notice period. You have asked for it you cannot do much more, follow it up with an another letter saying that you do not have a finish date and that you will continue to work on commitments.
At the moment everything is verbal. to formalise it send them a letter "following from our conversation I understand that i am fired but I am still to do work for you. I will continue to do this work at my previous salary".
Sorry to hear about the redundancy, I wish you the best for the future.