LED Driver Circut

What's the problem that is being experienced? By power leak, do you mean current is flowing from the 24V supply into the Pi somehow?

All the connections labeled 0V connect together between themselves, and go to to 0V (i.e. "-" connection) on the power supply. 

I just saw your other message. Regarding 

"unfortunately, I still have a leak because they gradually get brighter."

What happens when the resistor (100k or 10k) is temporarily shorted? Do the LEDs then fully extinguish during the time it is shorted?

If they extinguish fully during shorting, then the issue is left of the MOSFET. If they do not, then the issue is MOSFET related (either connections or faulty MOSFET).

If that test determines that the issue is left of the MOSFET, then you could try reducing the 220 ohm resistor to 100 ohm (if you don't have any 100 ohm resistors then you can parallel two 220 ohm resistors, because that equals 110 ohm which is close enough.

I'm curious as to why the design has the LED strip on with no input from the Pi?

I would think the strip would be OFF when the device is power-up and there no input from the Pi and are turned ON as the Pi controls them. Maybe I am missing something. I've tried to follow the whole design process that started on another thread and jumped to this for the solution.

I won't comment on the quality of that circuit. But the OP does have their circuit wired differently. The opto appears to be driving the gate high instead of an open-collector low. (maybe I am wrong)

There's another circuit on the other thread, with logic arranged such that the LED strip is off when the Pi is disconnected or is low. However, that circuit wasn't used. Someone suggested adding an optocoupler to the MOSFET. I merely showed how to insert that between the MOSFET, and the simplest way inverts the logic (which I mentioned at the time so that the OP was aware, in case it didn't meet the requirements). 

From the symptom (if I understood it correctly) there's a chance the MOSFET is faulty (easy to happen with ESD). The troubleshooting step mentioned above should rule that in or out, by forcing the gate temporarily low by shorting the 100k resistor.

If that test determines that the MOSFET is fine, then there's a chance the optocoupler needs more drive current into its LED, although I'd be surprised if it did - but worth a try, since reducing the 220 ohm resistor to 100 ohm for a test is unlikely to cause an issue.

i used this circuit becase the pi will always be connected and enclosed inside a toy i am making. I will be programming the toy to work automatically when plugged in.

P.S. that pic was my third try. my fourth board looks better. the PCB's i received from Amazon do not prevent all continuity between pins. I had to start using insulation on my tracers.

I agree the MOSFET is the issue

It might be worth ordering them from Newark/Farnell or any other big distributor, because some of the other suppliers don't take any ESD precautions when shipping them. If the MOSFETs are good when supplied, then to use them, I usually solder in the gate-source resistor (e.g. the 100k one in the diagram) first, so that the MOSFET is then a lot more protected while assembling the rest of the circuit (or solder in the MOSFET last).

Also, continually discharging yourself with a wriststrap etc is definitely worth doing if you have access to that. Also, the soldering iron can cause an issue, if it is a USB powered on (they don't have the tip grounded, which ends up with a high enough voltage that can damage MOSFET gates (a non-USB soldering iron is fine).

oh my gosh. I thought i was seeing things when soldering these up. i occasionally would see sparks. i never thought to ground myself while assembling the unit. 

Looking at PC817 datasheet it has a minimum current transfer ratio of 50%. From the scheme I see that with 0V on the mosfet gate the collector current of the transistor (PC817output) is about 9mA -> this means that the diode needs 18mA on worst case to be able to handle such output current! With 220Ohm series resistor however you're polarizing it with only 2mA, it has no chance to handle all the output current.

If you keep your 100k resistor and swap the 1k with 10k resistor the current that the optocoupler has to handle drops to about 1mA and should work (given that all other components are fine and not damaged by ESD as pointed out by others )

Beware that swapping 1k with 10k will slow down turn on transient, but I don't think it will be an issue...