I have 3 Roku devices installed on 3 TV's. I will be moving, do I disconnect these devices or leave them plugged in? What is the overall process?
You dont need to leave them plugged in. Unless you have extremely long cords.
Just move and we'll sort it out. At worst you'll need to sign back in to your Roku account.
There is no need for them to remain powered on all the time. They won't lose anything being unplugged. If they are connected by WiFi, there could be issues if new locations result in a weaker signal.