Did they know that

you were moving the the job location already? Did they know your current salary?  Why were you looking for a new job while having the old one?
Not sure how all these happened, but there is clearly mis-communication here.  On your side, you should have asked for firm offer, and get everything clarified before you do anything.  It is definitely a lesson learned for you.
On their side, it was un-professional if they knew you were moving and was still withholding your offer letter.  They probably have done nothing wrong on paper, but not very decent.  However, at this moment, you can only blame yourself.

You can go talk to them and explain to them what kind of undertanding and expectation you had before moving here, i.e. offer with salary matching or above, compensation for moving cost.  Now, since you didn't get what you have expected, you ask them  (nicely) why it is not.  If it is true, you can also mention to them that based on what you know. it is against the school policy to pay you such low salary, use that as a reason that you didn't question the salary before you come.  
 
If they would match your expectation, just tell them calmly that you can't sign the offer letter and you decided to move back at your own loss.

Do all calmly, no point loss temper with people like that.  But learn the lesson.