Way back in the 1950s when my parents bought a Levitt house on Long Island my father, who was a mechanic, took a course in fixing oil burners. The first night of the class, the teacher told a joke. He said that there was a guy who jumped out of an airplane and found out on the way down that his parachute didn't work. Pretty soon he saw a guy coming up from the ground toward him. As the guy got near he yelled out, "Know anything about parachutes?" As the guy from the ground whizzed past him he yelled back, "No. Know anything about oil burners?"
So pretty much since then I have left oil burners to the experts. Dad is not around now but I some mechanical guys in my life who and be consulted when needed. Since some of them (Richard) have moved to Florida, I'm resorting to a blog consultation. Here goes...

All this is attached to the oil burner as you probably know (she said hopefully). Water is dripping out of the opening that is labeled #1. I think it is is the overflow "vent." The number 2 is pointing to a little handle that will toggle back and forth. When I toggle it the right a bit of air comes out of the opening - #1. I left it open for a bit until it seemed like the air had stopped and nothing was happening. Number three has an arrow that points to the left and the handle (#2) as been left in that position. Number 4 - for clarification has "j flow" written on it in black magic marker. The pipe itself does not figure into the overflow (or whatever the stuff in the foreground is called).
It has dripped periodically, but not a lot and I put a 5 gal bucket underneath and mostly it never had more than a half inch of water. Today the bucket was full and some water was on the floor.
Got any ideas?
Wednesday Update: There is no water in the bucket. Either moving the toggle did something, left some pressure off (would have been slight) or the Smith's (my Dad) Law of Mystery Mechanics is in operation. Pop's Law states that if you don't know what is wrong with something, take it apart. If you can't see what is wrong with any of the parts, just put them back together and see what happens. Sometimes, for no obvious reason that fixes it and it works again. Of course, he never said it was magic. He just shrugged his shoulders and smiled. But I know better.