Looking for a slightly wacky but otherwise throw-away episode for your crew? Try this one.
The party's ship is in a stand-off with a hostile vessel, though not one at war with them. They are negotiating, but some fire is exchanged also.
Owing to the strange properties of the region of space (to keep the effect out of player-hands) and the interaction between the player's shields and the other ship's weapons, some energy gets through and has an odd effect on the crew. This odd effect is to cause people to exchange bodies, at random, with the peopel in the room with them.
Clearly they will want to figure out some way to reverse this process, which involves precise placement of people and persuading the other ship to shoot your ship.
In the meantime, humor can be derived by people not being able to tell who is who, and also people having to attend to vital bodily functions using unfamiliar equipment.
------------------
You're a Starfleet Officer. "Weird" is part of the job.