You may think the description is enough, but a FULL schematic (EVERY part and how its connected to the "nano" may show factors that havent been considered. Such as supply decoupling or circuit losses.
Are your LEDs all the same type and color? How (physically) are the grounds connected.
If you measure those voltages with a meter you will be reading the average voltage and as your program is generating PWM signals they arent immediately meaningful.
To test the hardware I'd suggest you run a VERY simple sketch just to turn each on in turn with a useful delay, or read in a number and turn on only that LED.
Different LEDs have different forward voltages, so it would be better to measure the voltage levels at the NANO outputs.
When you reference particular equipment its useful to post a link
I have just spent about a week debugging a similar issue using (I think) the same Arduino Nano board as you. Something I came across which did help is the analogReference() function. Check what the default voltage is for your board, it might not be the 5V you expect it to be - it wasn't for me!
There's more info in the arduino documentation about the options for different boards.