This is not what I'd consider the "oddest," but it is what I can document, a Rossin Ghibli on the back of a Trek 2120. Only 10 miles.
Soon I'll be trying an Oru Coast XT kayak on the back of my lime green '72 Super Sport, or my Lotus Odyssey, if I don't find a trailer first. Paddles too.
More recently, after loading up on cat litter and a huge sack of crunchies, lard, spud flakes, tins of tuna for the Murder Hornet Neko, and other groceries, I found a gorgeous wrought iron and solid wood meter tall table, and tied that to the top of everything. I had to shift my weight forward onto the bars to keep the bike from doing a wheelie the four miles home. It was late and the roads were mostly bereft of cars.
Yeah, I really could use a trailer...
I'm thinking an old Burley D'Lite, with a photo of a terrified child pasted in the rear window? (Around here, perhaps the appearance of towing a toddler might make me a little safer? I'll take what I can get.)