I would use a meter to double check like this:
Measure the resistance between the gray wires.
Measure the resistance between the red and black wires.
One should be much higher than the other (say 10x or more). The highest reading is the primary side which I would guess is the red/black pair.
For the instructions below, use a 1A fuse in the AC line to be safe and try and do this from a GFI protected outlet just in case you short or touch something you shouldn't.
Next, if the above checks out, put 115Vac into the the red/black pair and measure the voltage on the grey pair. If you read 3Vac then you've found the 230V connection and connecting to the yellow/black pair should be the 115V connection. If you'd read 6Vac, you had 115V pair already. If you only have 230V available use your ohm meter to find the highest resistance between the red, black or yellow wires and use that combo for a 230 trial.
As for the relay. Yes, it can switch both US and EU mains. Note that both those specs are probably for resistive loads only. Your relay will have a much lower current spec for lights, motors and inductive loads.