Legal Question in Wills and Trusts in Virginia

How would these liens against "everything owned besides [the] household

furniture" be satisfied and released if not through the process of probate?

Perhaps not. But there are some allowances the children may be able to claim by going through probate (which if the estate is insolvenet, may be quite a simple process). It may be worth a trip to the probate office of the local circuit court to present the facts and see what can be done.