This is not an answer to Tom asking you to supply a Schematic of your project. It is just a list of what wire connects to what between the ADC and your Nano. What it does not show is what other connections you have made to the ADC apart from these. If the answer is nothing then there is your answer.
That sounds to me what you would expect if you read the output of an ADC with nothing connected to its analogue inputs. When an input is not connected to anything, this is called a floating input. Due to the very high impedance of these inputs they will pick up all sorts of electro magnetic interference form the mains, near by wiring, and even radio waves.
This will produce a randomly fluctuating reading that you could very well describe as "all sorts of nonsense". So to get a reading of zero then connect all the ADC inputs to zero. If you want to get a reading then use a potential divider on the input pins to get the voltage you want to read. As these are very small values make sure the resistor ratio provides the correct voltage.
Points that would have been clear if you would have produced a schematic when asked for.
Another thing you need connecting to that chip is some decoupling capacitors. At least a 0.1uF between the power input and ground to that ADC chip. Here is a link describing the how and why of decoupling components. These are not optional in circuits.
http://www.thebox.myzen.co.uk/Tutorial/De-coupling.html
Now a bit of etiquette advice for this forum.
You might want to look at this How to get the best from this from this Forum before you proceed any further.
It will tell you how to post code correctly, I don't know what you are doing at the moment but all lines of code you post start with a > which is useless.
This is because even if we wanted to copy your code (and it was posted with the correct code tags) we would have to remove all the " >" at the start of each line to make it run on our machine. A simple global replace of > to nothing would risk removing some code especially in "if" statements.
All you need to do is to perform a "select all" in the IDE and then select "copy for forum" and then paste you code into your reply.
Also there is no need to use the reply button at the end of a post but just use the one at the bottom. Everyone following that post will get a notification.
Some are 5V and others are 3V3. It makes a big difference because the AD7730 is a 5V powered chip, that means it expects and produces 5V signals. If your Nano is a 5V one them (like the Nano Classic) it is fine you can connect the lines directly from chip to Nano. However if you have a 3V3 Nano, like any of the Nano 33 types (see the 33 is short for 3V3) or other types of Nano that work off 3V3 then you have to arrange level shifters in the signals between the Nano and the AD7730 pins. You can't connect them directly.