Yeah, oil is to the robot what food is to us Humans, and the oil lubrication to to keep the metal smooth moving, is the equivalent to Humans' physiotherapist!

The robots in your story surely adaped well to the rain! Bearing in mind that most technology right now is rather prone to any kind of dampness, we can assume that the inner wiring of robots will be reinforced in some way to become impervious to it! :)