It is true that your OPT expires as soon as they release your I-20. With the expiration of OPT, your work permit will also be invalid. You cannot work, legally. 

I would suggest:

i) Talk to the DSO from your previous school. If your SEVIS information  has not been updated yet, then I think you can still explain your situation and you MAY get away with it. But from what you are saying it seems to me that your SEVIS info has already been updated.

ii) Get CPT as soon as you can from any accredited university so that you don't have to stay away from work for a long time.

If both options above fail

iii) Go to Nepal for the extended summer and come back in new I-20 or H1-B, depending on the circumstances.