Allegedly, my dad's friend gave him $20,000 as a loan. He has since passed away with no money left in the estate. There are no written agreements or documentation on the loan, but my dad's friend is demanding repayment. Do I have to repay the loan?

If the executor of your father's estate believes the $20K loan is legit, then the executor should pay the loan back using funds from the estate. If there are no assets in the estate then the loan goes unpaid - there is no requirement that family members make good on the loan. However, even though you say he had no money there may be assets - did he have a car, a watch or other jewelry, furniture, or other personal possessions? These could be sold off to generate cash to pay the loan.

On the other hand - if the executor is unsure if the loan is legit, then given the lack of documentation I would argue that the executor's fiduciary responsibility to properly manage the estate's assets means he should not pay the loan off. Let the friend sue the estate and prove his case in court.

Did your dad's estate go through probate?

All assets have been sold to pay off other debts which is why there is no money left. The estate did not go through probate.

Then the friend has to sue the executor and heirs of the estate to recover the loan. He will have to prove the loan and also that his claim takes precedence over other debts.

If the heirs received no money and it all went to pay off debt, Its unlikely he will collect anything.

It will depend, debts and items to be sold normally are suppose to go though probate, and debts paid in certain order. Some types of debts get paid first, and others last. You don't owe them anything, you need to tell them to talk to the estate.
If there is nothing in writing, they will have to prove the debt. To the estate.

Who ever handled the estate may be in trouble if they did not handle the estate properly