Our family lives in a residence in Virginia. We have a 3 year lease with a private owner/landlord. We found out via public advertisement that the property is going to public auction. We have paid all our rent on time (2 weeks early actually) and have kept the property immaculate.

What are our options if our landlord dues not resolve this issue and the property sells at auction.

Do the new owners have to go through "due process" to evict us via Summons of Unlawful Detainment and subsequent Writ of Unlawful Detainment? Will I get a chance to plead my case i.e. Negotiate a possible lease with the new owner. Is the new owner required to get a Writ of Unlawful Detainment to evict us or can they just move us out? Puzzled and in a hurry!

The new owner does not have to honor the old lease,

You would be on a month to month rental with any new owner since there is no written agreement between you and them.

They would have to give you notice, and if you did not move, go to court to evict you. But you have no case to plead, since it does not matter what you did to keep the property up, does not matter you paid rent on time.

Once the gavel falls, all of the old agreement is void.
Normally the people doing the foreclosure would give you notice to move out, since you may not want 100's of people walking though your house looking at it prior to auction.

This is an unfortunate situation. Once the property goes to auction and there is a new owner, you are going to have to deal with the new owner. It may be an investor who will want to sign you to a new lease. It may be the bank that holds the mortgage or someone who wants to move into the house themselves. Only time will tell. Do you have a security deposit at risk? At this point, that is where your concerns should be channeled.