For follow-up discussion and general commentary on the topic. Comments are sorted chronologically.
This could be one of those "traditions" by Evangelicals that are not biblical. Pious, yes, but not biblical. The next question would be, "If the practice is not biblical, should we continue to practice it?"
The use of anointing oil has been abused by a branch of charismatics which falsely teaches that anointing oil should be applied on cars, houses and even clothes and offices to ward of any attacks from Satan. This is witchcraft in disguise.
The anointing can only be used by church elders in the manner anticipated in Scripture and for no other purpose.