The odds are very great that the house will NOT be sold at the Austion; very few are.
Which means that it will go back to the bank.
4-6 weeks later, the Bank will list it with a Broker for REO sale.
Figure at least 2-3 weels to sell, 2-3 weeks to be accepted and 45 days for Escrow;
Adding that up, you should not have to move until the middle of November.
When it comes time to move you out, the Realtor should contact you, probably with a 30 day notice. He will offer you some "moving money" which could be $1000 to $3000, to insure a timely move and with no damage to the house and it's contents. You won't get that money until after you move.
Please understand that these figures are just guesses, and could vary; but they are also minimums based on history. The good news, is that you will be contacted; it will not happen that a Sheriff's Deputy shows up on your doorstep one morning with an Eviction.
This is a very stressful time for you, at lot of good people have gone through this, and a lot more will. My heart goes out to you. Bounce back from this, do not let it get to you.
Good luck and may God bless