Arduino - Solar and Electricity Monitor Hardware Query

I don't entirely follow that, but you seem to have a combination of RS232 and USB and goodness only knows what's coming in over that RJ45 (Ethernet ?) going in to a PC where some unspecified software interacts with the inputs.

You need to have a lot more information about what protocols those interfaces use and what the PC application(s) do before you have any hope of replicating the PC functionality on an Arduino. Getting RS232 and USB drivers are the least of your problems, but for what it's worth you'd probably need an RS232 shield, and either a USB host shield or a Mega to provide a USB host port, and either an Ethernet shield (or Arduino with built-in Ethernet) or something capable of interfacing with whatever that RJ45 is presenting if it's not Ethernet. If it's Ethernet then you'd need to get a library (or write your own) to handle whatever protocols are being used on top of that.