Best of luck and I hope you close,
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I'm assuming that it is for the mortgage committment (and yes - banks can be slow). If this is the case then you can do no further unless they miss the deadline.
This is a very good example of why sellers should only get into contract with buyers who are a) putting down a minimum of 20%, b) have a LENDER's pre-approval with only two contingencies, a contract and an appraisal. This indicates they have gone through the full application processes and all of their documents have been verified and fit a mortgage program.
The oil company can be requested to measure the tank (they can do this from the outside) on the day of or before closing and they can fax the certificate to your attorney.
It does not make sense for a walk-through until you have moved out of the house. They will have to do one even if you have not moved everything out, but escrow will be held until a final walk-through is done and a release signed.
Make your moving arrangements; the movers are used to closings being delayed or cancelled for various reasons and if the closing does not happen, you will not have moved unless you so desire. check your contract to see if your attorney has given you an additional 5 days to remain in the house.
Your bank can provide you with a payoff number as late as when you are sitting at the closing table if need be. Do not stress this.
Your attorney will take care of tax adjustments.
It seems as if there is a lot to do, but just take one thing at a time. It is all attainable, but you need to stop looking at the big picture and start taking each task one-by-one.
If your contract demands a commitment by a certain date (or amount of days) and that time has passed, you have every right to have your attorney send a time is of the essence letter and you can ultimately severe your relationship with the buyers and start over. Is that really what you want to do?