I'm not sure if this qualifies as weirdest but it sticks out in my mind.
It's Eclipse Phase. In New Shanghai the players are investigating their own murders and have traced found links to a series of apparent morph implant malfunctions that cause spontaneous human combustion. They have two leads, a local escort who knows too much and a young free-runner/parcel delivery person who lives with a pair of uplifts at the only legitimate message parlor in the city. My players decide to go with a subtle approach and use the party face, an async obsessed with the color white, to ferret out the leads. What I didn't know what that the ferreting out would involve two, protracted Tac-Netted dating shows A La 1990's Elimidate.
We RPed out a full escort contract negotiation scene, complete with suggestions from the teammates via text message. The team mates knew about the async's mind-powers so they were guiding them through the process of arranging for some casual BDSM. They negotiated for an interrogation scene which the async used to ask priming questions for throughtbrowsing. When that didn't work they knocked them out and did a full probe. They left a heavy tip behind.
Next up they had the async "date" the free runner. They intensely researched this freerunners social media profiles and discovered that they were into female-presenting morphs and were sorta adopted by a gorilla uplift masseuse. They arranged a chance encounter at the message parlor, literally scripting a meet-cute followed by a date to the freerunner's favorite noodle place (which they had already pulled from social media). The team fell into "date small talk suggestion mode" and ended up RPing an entire first date, forgetting their objective.
So they had to arrange for a second date.
The second date was overwatched by the gorilla who was lurking a block back because he didn't trust this strange, pale weird human with his adopted daughter. Half the team ended up trying to distract helicopter gorilla dad while the other team kept up the small talk advice while they strolled through the souks. Finally the two teams came to a head when gorilla dad ended up blundering through the date, triggering a panic attack from the free runner. The async picked up on the free runners nascent pyrokinesis as a wandering noodle-dispensing robot erupted in steam, filling the scene with clouds of chicken-scented mist.
Time and other commitments ended up killing the campaign but I wish I could go back and see how many more dates they would have ended up getting the async to go on.
