Stenbock was the count of Bogesund and the heir to an estate near Kolga in Estonia. He was the son of Lucy Sophia Frerichs, a Manchester cotton heiress, and Count Erich Stenbock, of a distinguished Swedish noble family of the Baltic German House of nobility in Reval. The family rose to prominence in the service of King Gustav Vasa: Catherine Stenbock was the third and last consort of Gustav Vasa and Queen consort of Sweden between 1552 and 1560. Stenbock's great-grandfather was Baron Friedrich von Stuart (1761–1842) from Courland. Immanuel Kant was a great-great-granduncle of Stenbock.
Stenbock's father died suddenly while he was one year old; his properties were held in trust for him by his grandfather Magnus. Eric's maternal grandfather died while Eric was quite young, also, in 1866, leaving him another trust fund.
Stenbock attended Balliol College in Oxford but never completed his studies. While at Oxford, Eric was deeply influenced by the homosexual Pre-Raphaelite artist and illustrator Simeon Solomon. He is also said to have had a relationship with the composer and conductor Norman O'Neill and with other "young men".
In Oxford, Stenbock also converted to Roman Catholicism taking for himself the name Stanislaus. Some years later Eric also admitted to having tried a different religion every week in Oxford. At the end of his life, he seemed to have developed a syncretist religion containing elements of Catholicism, Buddhism and idolatry.
In 1885, Count Magnus died, upon which Stenbock, as the oldest living male relative, acceded to the status of Count and to the possession of the family's estates in Estonia. Eric traveled to and lived in Kolga for a year and a half; he returned to England in the summer of 1887, during which time he sank deeper into alcoholism and drug addiction.
Stenbock behaved eccentrically. He kept snakes, lizards, salamanders and toads in his room, and had a "zoo" in his garden containing a reindeer, a fox, and a bear. When he traveled, he invariably brought with him a dog, a monkey, and a life-sized doll. This doll he referred to as "le Petit Comte" ("the little Count") and told everyone that it was his son; he insisted it be brought to him daily, and—when it was absent—he asked about its health. (Stenbock's family believed an unscrupulous Jesuit had been given large amounts of money by the Count for the "education" of this doll.)