Are there any UL requirements regarding wire attachment to PCBs?
Is it permissible to directly solder a wire to a PCB?
If so, what kind of strain relief is required?
Unless the specific standard your device is being designed to calls for something specific there is no requirement to do anything but solder it directly to a PCB (as shown in your image #1).
No strain relief is required by UL at all..
We have hundreds of UL listed products where we simply solder anything from 24 to 14 AWG directly to the board without any relief at all. Never had a problem.
Now depending on the environment/vibration,etc.. that your specific product might see in its lifespan it would probably be a good idea to do something like #2 or other but its not required generically.