On the contact side of the relay you'll need to be able to switch at least 24V and at least i = p/v = 8W / 24V = 1/3A, if I understand you correctly. Are the three load devices inductive? Is there a significant inrush current when you turn them on? We need this information to really fully determine their current requirements, but over-sizing this relay shouldn't be too costly anyway. If you want to be really really safe, maybe just get 5A relays like the Barix device has, then you'll extend its capabilities in a consistent way, which could be useful later on.
If the power supply is outputting 24VDC at a maximum of 2A, it should be 48W, not 120W, so we're probably missing something as far as the power supply goes. Does it have other output voltages, and 120W is the total?
You need to think about current on the coil side of the relay as well. Will you be using the digital outputs of the Barix device for this? These are open-collector which is very suitable for turning on relay coils, but you'll need to find out what the current and voltage limits of these outputs are, and make sure your chosen relay doesn't exceed these.
To do this right you also need to consider that the coil is an inductive load, and put a snubber network of some type across the coil. A simple rectifier diode will probably suffice, but putting a zener in series with the rectifier is better since it will allow the contacts to get moving faster upon release, which means the relay will last longer.
