To bedevil is to "be" a bit like a "devil." To bedevil means to cause trouble, or, when talking about a person, to torment or harass.
Bedevil has nothing to do with the eggs you eat on a picnic. Those are just plain deviled. And although, in the 1570s, bedeviled could be taken to mean literally "possessed," the word no longer involves an actual devil, either. It just applies to people or things that make trouble like a devil would want to do.