We also have a HUGE green squashy sort of thing that volunteered itself from our compost and none of us have any idea what it is. Even our garden expert neighbour is stumped by it. It grew through the open window of our greenhouse, along the path, and into our neighbour's greenhouse (which is only a few feet away). There's only the one fruit on it, but it's massive. We're afraid to fall asleep anywhere near it....
How big is it?
I occasionally see some really weird, large squashlike things at the farmer's market. I don't know if anyone ever buys them, or only uses them for decoration if they do buy them.
Once I bought a really large Armenian cucumber. I had to cut it into 4 pieces in order to fit it in the refrigerator. It was not good. It was full of woody seeds and the flesh was crunchy, but very dry and tasteless.
I also bought a big Daikon radish. It made good pickles, though it took 4 batches of pickles to use it up.