As far as I know, in most situation, if you plan on transfering to another school or get a H1B, you need a statement from your current school to prove you are still in status. The expiration date of the I20 does not mean much in this case. With the SEVIS system and all the strict rules regarding foreign students now, I think the most important thing for you now is to work out with your current school. If they insist you are out of status and are not willing to help you, it is going to be hard for you.