If you read the "Dropping to 0 Hit Points" section of the PHB/basic rules, you'll find the following paragraph under "Instant Death":
Massive damage can kill you instantly. When damage reduces you to 0 hit points and there is damage remaining, you die if the remaining damage equals or exceeds your hit point maximum.
Thus, the "killed outright" that the Half Orc's racial trait is referring to here is overdamage equal to your Hit Point max.
Death Ward will trigger the first time you drop to 0 hit points, and Relentless Endurance won't. Then next time you drop to 0, Relentless Endurance will be ready to go.
Death Ward, emphasis mine:
The first time the target would drop to 0 hit points as a result of taking damage, the target instead drops to 1 hit point, and the spell ends.
As soon as you would be reduced to 0 HP, you are instead reduced to 1. As opposed to the Relentless Endurance trait, emphasis mine:
When you are reduced to 0 hit points but not killed outright, you can drop to 1 hit point instead. You can’t use this feature again until you finish a long rest.
You choose when to use it. It doesn't automatically trigger when you are reduced to 0 HP. So when you are reduced to 0, with both Relentless Endurance and Death Ward, just don't use Relentless Endurance. Death Ward will be used, then next time you drop to 0, you can use Relentless Endurance.
There's another point to be made here, though. Even if you want to use Relentless Endurance, while you have Death Ward on, you can't.
The first time the target would drop to 0 hit points as a result of taking damage, the target instead drops to 1 hit point, and the spell ends.
Death Ward triggers when you would drop to 0, and makes you drop to 1 instead. You never actually drop to 0.
When you are reduced to 0 hit points but not killed outright, you can drop to 1 hit point instead. You can’t use this feature again until you finish a long rest.
Since Relentless Endurance is triggered when your hit points are reduced to 0, and Death Ward prevents you from ever reaching 0, you couldn't use Relentless Endurance even if you wanted to. This argument also works if your DM believes you don't get to choose when to use Relentless Endurance, which you asking this question suggests he does.
Best Answer
Relentless Endurance does not trigger if you die.
Relentless Endurance states:
Soul cage has a casting time of 1 Reaction:
If you are using Relentless Endurance, at no point are you dead, so at no point are you an eligible target for soul cage. If you are dead, then you can't use Relentless Endurance, and would be an eligible target for soul cage.
Soul cage only works when a humanoid dies, Relentless Endurance only triggers when you don't die, so there is no interaction between these two features.
To answer the question directly, Relentless Endurance can indirectly protect you from soul cage by possibly delaying your death, as instead of being knocked unconscious and rolling death saves when you reach 0 hit points, you instead have 1 hit point.