over the vending machine seems to make least sense here. I am not aware of any idiomatic meaning of it, and to literally hear it over the vending machine, Jeffrey has to be quite tall, or the vending machine has to be considerably smaller than most that I have ever seen.
over tea would actually be an option.
I discussed the proposal with John over lunch.
Is a sentence no-one would think to be strange, meaning that I discussed it with John while I was having lunch with him. If I had tea with him instead of lunch, I could say I discussed it over tea.
If someone told Jeffrey the news while they were having tea, one could say Jeffrey heard it over tea.
over the grapevine I usually hear as on or through the grapevine. I actually had to google to see if over was used, but it seems it is. It doesn't seem to be very popular though. However, if we assume that over the grapevine is the same as through the grapevine, this is the most likely answer.
through the grapevine is indeed idiomatic, and it means that you heard rumours about it.
over the fence could literally mean someone told Jeffrey something while they were on opposite sides of a fence, but I would be surprised to hear it regularly used. The phrase over the fence I would normally associate with movement: he hit the ball over the fence.