I'm not descended from any Whillans or Oliver myself, and my closest connection to both surnames is that my great-grandmother Martha Stewart from Hawick had a sister, Jane Murray Stewart, who in 1872 married a George Whillans at Upper Samieston, Jedburgh.
George Whillans was the son of George Whillans and Mary Oliver who were married in 1833 at Camptown, Jedburgh. Mary Oliver died in 1888 and her death certificate gives her parents as Robert Oliver, joiner, and Elizabeth Robert. I haven't found a marriage for this couple. Maybe Mary Oliver was illegitimate, although the death certificate says that Robert was her mother's M.S. (maiden surname).
Harry