You need to get a copy of the will and get it in front of an attorney for review. The oral statements prior to your parents death really have no legal significance (absent other facts not presented), and even if there is no will the executor would generally divide the assets equally among the children. Has anyone qualified as executor? If so, you can obtain a copy of the will from the circuit court clerk's office. Get this copy in front of a local attorney and discuss all the facts with them so they can understand exactly what is going on and explain what remedies may be available.
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DISCLAIMER: THE INFORMATION PRESENTED HERE IS GENERAL IN NATURE AND IS NOT INTENDED, NOR SHOULD IT BE CONSTRUED, AS LEGAL ADVICE. THIS POSTING DOES NOT CREATE ANY ATTORNEY-CLIENT RELATIONSHIP BETWEEN US. FOR SPECIFIC ADVICE ABOUT YOUR PARTICULAR SITUATION, CONSULT A QUALIFIED ATTORNEY.
Your question is not enirely clear. I assume that you are asking if some of the children, excluding at least one of the children, can simply decide how to distribute the property regardless of what the Last Will and Testament says. Perhaps I am oversimplifying your question.
If I am accurately restating your question, then the short answer is "no."
The oral agreement to distribute assets in a certain way has no validity unless someone relied on the agreement to his or her econoic detriment. There may be a theory of "quantum merruit" in a case like this. I don't believe Virginia allows such an action. It is worth mentioning to an attorney if there was some reliance on the promise, however.
I think the first issue is that the children who want to make the decision don't have the authority to do so. Any deed will require the signatures of either the Personal Representative/Executor of the Estate or all of the heirs (or both). To make decisions like this, the Court has to grant authority to you (or someone) to act. You can't just give yourself the authority to act regarding your parent's property.
Second, what does the Will say? In Virginia, Real Estate drops through probate and vests in the heirs subject to the claims of creditors, unless the decedent's Will specifically states otherwise regarding the real estate. If this is the case, all of the heirs will have to sign a deed conveying to certain individuals.
Third, in order to distribute property in kind, either the Will must give authority to do so or someone should probaby put together an Agreement regarding the distribution, particularly if one of the children receiving the real estate is also the Personal Representative/Executor.
To hammer out these issues, you really need to consult an attorney who is very familiar with the Virginia probate process. This general information is just that, general. Your particular facts and circumstances will impact how an attorney advises you to proceed. My response is based on general law and not specific to the many variables your situation may include.
Best of luck resolving your matter.