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.

Yes, your Half-Orc Barbarian is nigh-invulnerable to death by falling, as a consumable resource.

Remember that your relentless endurance and your rages both recharge on a long rest. So four times per long day you can take a header off a skyscraper and be pretty sure of living.^* (At least for the moment.)

Also, your Bard and Wizard friends can do this, too. Along with five of their friends.

It's called feather fall.

Point being: you can spend your consumables on base jumping without a parachute, and they can spend theirs on doing it with a parachute. You just get a bigger adrenaline rush out of it. (And the accompanying exhaustion.)

^{*- How sure? Assuming you start at 6HP or more it's impossible to instantly die from rage-jumping massive damage: the fall would need to do 61 damage after reduction, which is impossible for the mere 20d6 you're looking at. You may be at 0HP and looking at some death saves, the odds on which are not nearly as good**}.

^{Relentless-jumping is a little riskier on the front-end, but you do walk away. At full HP you're looking at ~0.0000003% chance of instantly dying of massive damage, at 1HP you're looking at ~13.4%, if I'm reading my first anydice program correctly. It's non-linear between those two endpoints, and in your favor. Check out the graph if you want to see.}

^{**- The probability of surviving death saves unassisted is ~60%.}