I2C looks better to us.
digitalWrite (ssPin, LOW);SPI.transfer(on_off_state0); // repeat for each boarddigitalWrite (ssPin, HIGH);
Can use shiftOut() also if the D50-53 pins are not available for SPI on the Mega.
Is it SPDT? Contact rating?
Your basic observational powers are severely lacking... it's a custom board with a very nice photo that had you spent 5 seconds observing said photo you could have clearly seen the relays are Omron G5T-1A. SPST 5A 250V AC.I wonder how many I2C relay boards you've ignored...