|Church of St. Walburga in Eichstadt, Bavaria|
Many saints have this phenomenon associated with them. The earliest was St. Paulinus of Nola, who died in 431.* Oil was poured over his relics, and then collected in containers and cloths and given to those in need of cures. The historian Paulinus of Pétrigeux (writing about 470) tells us that by his day this practice was being used on relics of saints who were not martyred as well. The relics of St. Martin of Tours (316-397) were used in this way. St. Augustine of Hippo (354-430) records that a dead man was resurrected in this way by use of oil of St. Stephen, the first Christian martyr who was stoned in 34.
One of the most famous oils is still "in production," as it were. In Eichstadt in Bavaria, at the Church of St. Walburga (c.710-779), a liquid flows from the stone and metal on which are placed the relics of this saint. The church is owned by the Sisters of Saint Benedict, who collect the liquid and give it away in small vessels. This fluid has been analyzed and discovered to be nothing more than water (suggesting that it is created by condensation from humid air on a cool slab), but its contact with the saint's relics make it valuable to the faithful.
Another source of "oil" is the relics of St. Nicholas of Myra. His relics in the Church of San Nicola in Bari produce a fluid called "Manna of St. Nicholas" and believed to have curative properties.
Most accounts of "Oil of Saints" are connected with saints from the first several centuries of the Common Era, with only one each from the 11th, 13th and 14th centuries.
*St. Menas lived and died earlier, but the curative properties of his burial place were not discovered until later in the 5th century.