Yes, they do
The Shadow Magic sorcerer's Strength of the Grave feature (XGtE, p. 51) reads:
When damage reduces you to 0 hit points, you can make a Charisma saving throw (DC 5 + the damage taken). On a success, you instead drop to 1 hit point. You can’t use this feature if you are reduced to 0 hit points by radiant damage or by a critical hit.
After the saving throw succeeds, you can’t use this feature again until you finish a long rest.
The Half-Orc's Relentless Endurance trait reads:
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.
Nothing about these abilities explicitly prohibits the use of the other. If you fail the save, you would still drop to 0 HP which satisfies the condition for Relentless Endurance's use. As a result, you can use both abilities if Strength of the Grave fails.
This matches the rules intent, as confirmed in an unofficial tweet by lead rules designer Jeremy Crawford:
are features like barbarian relentless rage and shadow sorcerer strength of the grave intended to stack (if you fail one saving throw, try the other) or is it a choose one in an instant scenario?
Things in the game don't shut each other off unless a rule explicitly says otherwise.