Not exactly strange freight as such and no, I wasn't flying, but how about using a corporate jet to get a dozen car windscreen wiper blades from Germany to Detroit?
Totally true story and I will name neither party for obvious reasons, but ...
.... for once Teutonic efficiency hadn't been in operation when their new car models were shipped out there for the 20?? motor show....Err, just sans windscreen wipers = last minute panic and a very happy charter broker, who paid for our business lunch, after gleefully explaining the details!