[RPG] Can Truesight (as from the True Seeing spell) see through the Hunger of Hadar or Darkness spells

If the Warlock is inside, NO. If they are outside, Maybe.

The real key here is the wording on Hunger of Hadar. The spell breaks itself down into being inside the sphere, and being on the outside looking in. We'll use that same breakdown as well.

(emphasis mine)

A 20-foot-radius sphere of blackness and bitter cold appears, centered on a point with range and lasting for the duration. ... No light, magical or otherwise, can illuminate the area, and creatures fully within the area are blinded. - *Hunger of Hadar, Player's Handbook

Inside

If you are fully inside of the sphere you have the blinded condition. Devil's Sight does nothing to counteract that condition.

“A blinded creature can’t see and automatically fails any ability check that requires sight

Outside

This is where the RAW gets fuzzy. As Justin T mentioned,it would be a DM discretion issue on "blackness" being the same as "darkness". Within the text of Hunger of Hadar it mentions opening "a gateway to the dark between the stars". This uses the word dark, so I would probably rule that you can see into it. At the end of the day though, it would be up to your DM.

The spell is very good, in the right circumstances or against the right opponents. The use cases are:

• You're fighting an opponent with significant defences but not a lot of HP. Cold is rarely resisted by enemies (so far), and the cold effect neither allows a save nor requires an attack. That 2d6 damage can affect almost any creature with no chance of failure, at least once.
• You've cornered the enemy (or they've cornered themselves). If you can fill the enemy's region of the battlefield entirely with this spell, and your allies can block off the only way(s) out, then the enemies are probably dead, even if they were significantly above your level. They can't leave the area because your allies are in the way, and they are unlikely to hit your allies because they are blinded (no save), while your allies have neither advantage nor disadvantage to hitting them via the cancellation rules. Each turn they all take 2d6 cold damage (no save) and maybe 2d6 acid damage. The spell lasts up to a minute so that's definitely 20d6 cold damage to everything in the area, and maybe 20d6 acid damage as well, if the spell plays out its entire duration. Two full castings is enough to take out an adult red dragon, if you could somehow keep it stuck in the area. That's two castings of a third level spell possibly taking out a CR 17 creature. Now, this use case is pretty uncommon unless you set it up yourself, but you can usually set it up pretty okay for encounters that take place in small rooms, by having allies close and bar the doors immediately after your casting.
• You're fighting zombies, skeletons, or other mindless creatures that just march towards you and attack no matter what. You can set up a perimeter where they stand in the bad stuff and you don't and kill them all just as if they were cornered, except you don't have to block off the exits and in fact may want to not do so to allow more of them to pour in. Given their speeds, hps, and saving throws, skeletons won't even make it to your line half the time, and Zombies will die before getting there more often then not. Especially if you are playing certain older D&D modules, where these creatures may be encountered in groups of !50!, a single spell easily capable of slaying as many as 320 such undead with a single casting is quite formidable.
• You need to escape down a tunnel, street, or similar linear path less than 40 feet across. While most enemies are smart enough not to wander into the spell's area and stand there, you can use that to your advantage. Cast the spell behind your party while you are fleeing, and have your allies guard the edge as above for a round or two. If the enemies try to force their way through, you keep them back and kill them all. If they don't, you flee and they are delayed for several full rounds before they can follow you. Even with enemies who you can't fight at all, the total concealment and area of difficult terrain can help your party out significantly, even though it means not dashing for a round.
• Your party is fighting a single opponent in melee in the open and have it surrounded. Maybe it's the big bad, if not this is probably a waste of a third level slot. You cast the spell 43 ft or so above your opponent, blinding and damaging them but leaving your allies uninhibited. They all have advantage on attacks v.s. the enemy, who has disadvantage on attacks and takes 2d6 or 4d6 damage a round.
• Your last name is Whateley. The spell doesn't just kill and blind stuff, it opens a gateway to the dark between the stars, the realm of the Great Old Ones. If you were hoping to call forth the spawn of Yog-Sothoth, Shub-Niggurath, or similar beings, the spell would be a good place to start. Indeed, you can actually hear whispers and stuff through the Gate-- possibly they can hear you too. Certainly, if you were so inclined and properly prepared, you might eschew the typical uses of the Gate for one-way travel to said realm of Utterdarkness and Insanity. The consequences for doing so, and the likelihood one any particular entity or entities crossing through the portal while the spell is active normally, is a matter of setting.
• You wanna kill a Godling. Say you're a Warlock with the Great Old One patron, or your BBEG is a Warlock with a Great Old One patron (or just a Great Old One), and you've decided that Great Old One's gotta die. This spell lets you (depending on the Old One) pop open a portal to where it is, so you can throw stuff through without actually going there. Maybe, like, oil and a torch? How many hp does The King In Yellow have, anyways?