Oelhafen was born in the manor of Eismannsberg near Altdorf belonging to the noble family of Oelhafen von Schöllenbach, his father Christoph Elias (1675–1736) was a lawyer married to Anna Maria née Gwandschneider.
His younger siblings included the future Field Marshal of the Franconian Imperial Circle Georg Christoph Oelhafen von Schöllenbach (1710–1779) and the Court Councillor Jakob Christoph Oelhafen von Schöllenbach (1712–1749).
Carl Christoph studied at Altdorf between 1724 and 1732 and then travelled across Europe as part of the academic grand tour.
He took an interest in fruit and timber trees and was involved in establishing plantations and forestry across Franconia.
He translated the works of Henry Louis Du Hamel du Monceau including De la Physique des Arbres (1758) into German[1][2] and also wrote on the wild trees of Franconia.