One of the plug-in protectors I am using has 3 MOVs with a rating of 590 joules each, 1770 joules total
Surge protector "energy" ratings are not additive. Only 1 surge diverter will ever fire at a time.
It doesn't matter whether you have 3 or 10 or 100 varistors built into a surge protection device. Only the most sensitive one will fire, and if the energy released by clamping the surge exceeds it's capacity, it will be incinerated. This is the case even when using "binned" varistors - the variation within a single bin will typically result in 1 varistor taking 99.9% of the surge energy, even when paralleled with multiple "matched" varistors.
MOVs are voltage limiters, and their current smoothly (but rapidly) rises when the voltage increases (they don't "fire"). They can conduct thousands of amps for a very short time. The voltage will then be significantly over the nominal clamp voltage.
If the MOVs are connected in parallel one is likely to conduct at a lower voltage. High current drives the voltage higher, which causes MOVs with close clamp voltage characteristics to conduct. If using MOVs from the same manufacturing lot the characteristics are pretty similar and I would expect the surge to be largely shared. If not from the same lot not likely. (Paralleling is a side issue.)
But a plug-in protector has separate MOVs connected L-N, L-G, N-G. This is detailed in the IEEE surge guide. That would be how my 590J MOVs are connected. If there was a strong surge entering on power service wires, the hot wire rises with respect to the neutral and ground (there is a N-G bond at US services). Both the L-N and L-G MOVs will conduct. The N-G MOV may conduct depending on its voltage rating.
Of course, the "surge energy" rating of a surge protector isn't really that useful a measure, as it is an aggregation of all the more important parameters of the protector: namely surge diversion current, maximum surge duration and clamping voltage.
MOVs accumulate damage and the joule rating is useful because it indicates how much damage they can withstand. (Cumulative ratings are likely much higher than the single event rating.)
Surge current ratings are equivalent to the joule rating. If you have a service protector rated 10,000 surge amps and there is a 10,000A surge the protector is likely at about end of life. The 590J MOVs in one of my protectors have an equivalent surge current rating of 30,000A. That is far more than you can get on a service wire.
The surge energy isn't actually dissipated by the protector - it is diverted away from the protected device. This means that the actual amount of surge energy that can be protected against is much higher than the rating of the protection device.
I don't think this is as much appreciated as it should be.
[Westom thinks plug-in protectors work by absorbing the surge.]