I happen to have a copy of Tales from the Yawning Portal, published after you posted this question, and it indeed contains the adventure module Dead in Thay. It is not quite the same adventure module as was used in D&D Next, with a few parts of the adventure omitted or modified. Regardless, the introduction to the adventure in Tales from the Yawning Portal, plus a few other details scattered throughout the module, contains a window into the activities and personalities of the Red Wizards of Thay.
I will admit up front that the information from this module is quite limited in scope, so probably doesn't constitute the 'best' source, but it is an official source current to 5E, and the only one I have. I will summarise the key points below. Some elements could be considered spoilers for the adventure, so I have put them in hiders. You will want to consider whether your adventures take place before or after the events of Dead in Thay.
We are given some history. Kazit Gul was a Thayan archmage who eventually became a lich. He engineered the Doomvault, a massive dungeon deep beneath the Thaymount, with the intent of luring in adventurers and harvesting their souls. As Thay became more hostile to outsiders, fewer people sought the Doomvault, and Gul became a demilich. At some point, Szass Tam and his followers defeated and enslaved Gul. The Doomvault has since been re-purposed it into an evil lair, where the Red Wizards perform experiments and build their armies.
Hidden beneath the Doomvault is the Phylactery Vault. Within the Phylactery Vault are the phylacteries of Kazit Gul, Szass Tam and all his elite lich servants.
By the end of Dead in Thay, the Phylactery Vault and all the phylacteries within are destroyed. It is ambiguous as to whether Szass Tam's phylactery was also destroyed, or whether it was somewhere else, as Szass Tam's phylactery is mentioned only once while all other mentions of the Phylactery Vault only refer to Szass Tam's elite liches.
At the time of the adventure, the master of the Red Wizards of Thay was the lich lord Szass Tam. We do not meet Szass Tam in Dead in Thay, but we are told a fair bit about his schemes. He is attempting to conquer the North then all of Faerun. He is also seeking god-hood.
We learn of another character: the lich Tarul Var. He appears to be a general, with Szass Tam as his master. Var was in command of Bloodgate Keep and the attempted invasion of the Sword Coast. After failing at Bloodgate Keep, Var fears Szass Tam, who will probably punish him. We are told a bit about Var's personality.
Devious and arrogant, Tarul Var thinks all other creatures are beneath him. He berates the characters at every opportunity, and he drives his underlings to cruelty.
As for Var's fate,
Tarul Var may or may not be dead at the end of Dead in Thay. This depends on whether the player characters kill him or let him live, and whether they destroy the Phylactery Vault before he rejuvenates.
The adventure module names a few Red Wizards who aren't liches, but they probably aren't that important outside the Doomvault.
There is one other major character among the Red Wizards, who reveals that Szass Tam's leadership is not absolute, and that is Syranna, a leader in the Thayan Resurrection resistance movement. From the information provided, the Thayan Resurrection appears to be run by Red Wizards who are dissatisfied with Szass Tam's leadership and are rebelling against him. These Red Wizards are probably regarded as renegades and rebels by other Red Wizards.
Syranna had some noteworthy words to say about Thay and Szass Tam.
"Many Red Wizards chafe under the rule of Szass Tam. Once, Thay was a land of learning and power. Now, death scours Thay while the lich lord ignores all concerns other than his quest to become a god. If his mad plans are left to run their course, none will be left alive here to worship him."
After the events of Dead in Thay,
with the Phylactery Vault destroyed and the Doomvault in disarray, much of Szass Tam's power is broken. 'She invites any characters who proved useful, particularly those with arcane talents, to remain in Thay under her leadership. She promises them power and influence if they throw in support for her.' From this, we can infer that Syranna plots to overthrow Szass Tam, and if successful she would be the leader of Thay after Dead in Thay, not Szass Tam. As lawful neutral, she probably won't be trying to conquer the world like Szass Tam. Probably. But she's still a Red Wizard, so they'll still be doing some Red Wizard things.
In summary, Dead in Thay tells us the following key pieces of information about the Red Wizards of Thay: Their leader is Szass Tam, a lich lord with plans for conquest and godhood. Tarul Var is one of Tam's generals, and also a lich. Working against Szass Tam is the Thayan Resurrection, a Red Wizard-led rebellion, with Syranna as a key leader.
Short Answer: You can consider the adventures mostly ordered in terms of difficulty as well as character level, but not all of them are "the deadliest in history".
Tales from the Yawning Portal is an excellent book; a collection of some of the great adventures in the history of Dungeons and Dragons. You're looking at a source for seven adventures, all varying in difficulty and length. The promotional description may be a little generalized though. The better description is A collection of exciting and challenging adventures that gives DMs resources for one off adventures for all player levels. Sure, Tome of Horrors are only for DMs looking to eliminate player characters, but the others run differently, and each are challenging in their own way.
The Sunless Citadel and The Forge of Fury are the lowest level, and (relatively) easiest adventures of the book. Citadel is a great one off specifically for 1st level characters. The Forge is perfect as an immediate run right after The Sunless Citadel. These are perfect for teaching new players or those with difficulty with traps on how to handle themselves properly in dungeon crawling. Deadly rating: Not so much. Average difficulty.
The Hidden Shrine of Tamoachan is the next adventure in character level, but definitely takes a climb up in difficulty. Traps are devious. The treasure inside is a little sparse, and may not be worth the danger inside. Even if the players survive the adventure, there is a chance that the dungeon can trap them in, and force them to be new slaves for Tamoachan! Deadly rating: Deadly. Beware.
White Plume Mountain mellows out the challenge a bit, taking an expected challenge for its level range. If the party keeps a level head, the incredibly creative puzzles and environment encounters are not too overwhelming. They are definitely creative, and usually do not take a linear approach like standard traps. So if your players are not used to handling that, it will be difficult! Deadly rating: kinda deadly.
Dead in Thay is really a series of adventures in a super dungeon, and expect this one to compete with Against The Giants for the longest. This one is a collection of very creative "rooms" that all rolled up into a marathon of encounters that will drain your players of their spells and powers per day. Resource Management will be the silent killer in this one. Pay attention to the risk of character death in this place, because if certain conditions are not met, any resurrected character will find their souls trapped forever! Deadly rating: Deadly
Against the Giants is another one that really is multiple adventures. It is three different modules, that will send the players on a tour of the different types of Giants. All of the Giants are dangerous in their own way, so if the players do not adapt their tactics and evaluate their enemies, then they could find themselves in trouble against one type or another. The difficulty evens out for this one though, as it offers some separation between modules, which means a change to rest and recharge - something not readily offered in Dead in Thay Deadly rating: Not so much, Average.
Tomb of Horrors ... Evil. Just ruthless and pure hate. Run this if you promised your players that you would kill some of them. If your players have any trouble with handling traps or figuring out puzzles, it's all but guaranteed to be deadly. There's false entrances that may even be trapped that prevent the party from even entering! Inside, there's a seemingly innocent trap that levitates a player... into a chamber where their only real options are to starve or die of thirst, or run into another room to be assuredly chopped to bits. Then, there is another trap with a chance of being magically stripped of all of your possessions, and then teleported out of the dungeon entirely. Those are just two of the thirty-something encounters of this dungeon. 'Nuff said. Deadly rating: Over 9000. Side effects include: possible rash, intense weeping, may ruin friendships.
Best Answer
Best Estimate: levels 10–14
In Dungeon Magazine #213, April 2013 Chris Perkins published a conversion of the Tomb of Horrors for D&D Next.
From that magazine:
I went through the adaptation in Tales from the Yawning Portal and did a rough compare, and for the most part, it is a direct conversion. In some cases the original module has higher DC checks, or the traps do more damage; as befitting the D&D Next rules in play around that time. But the monsters are effectively the same.
I feel pretty safe saying you can use those levels as your guideline. Go a smidge lower if you want it to be harder.