I suspect that you have a fundamental misunderstanding of the 'internals' of the Nano board. Can you provide drawings for the different scenarios that you described.
Your Nano pins don't provide 12V (as you show in your drawing), they provide 5V (regardless what you put in).
2)
Providing 12V (on Vin) and USB power at the same time as you do in the current drawing is quite useless; the 12V will power the Nano.
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How many leds per strip? Are those led strips 12V or 5V? A link would be useful.
You can only safely source (drive) around 20mA out of each of the pins (so that's about one led, maybe two leds), the maximum for the microcontrollers Vcc is 200mA and the maximum output current for the voltage regulator on the Nano is around 150mA (if I'm not mistaken).