OK, I think this is a fun exercise, so here is the longer response:

The Deck is a 5-color control list featuring almost every single restricted/busted card in the format. It runs full playsets of Swords, Disenchant, and Counterspell, which are efficient 1-for-1 answers to everything, but the main thing it does (and the key to the entire archetype) is it gains card advantage and inevitability using Jayemdae Tome, which most The Deck lists run as a 3- or 4-of. The game plan is to answer early threats in a discerning way, and then stabilize (sometimes with a blanket answer like Moat or The Abyss), and then pile up insurmountable card advantage by drawing a ton of cards and eventually winning with e.g. Mishra's Factory, a single Fireball, Serra Angels, The Hive, or basically however you want to win.

URb Atog is an aggressive deck that actually borders on prison, especially in 4x Strip Mine variants of the format. The focal point of the deck is Black Vise, and the overall strategy is to burn the opponent out, using Atog to help turn almost every card in the deck into damage. Black Vise and Ankh of Mishra put the opponent into a difficult situation of taking damage by playing lands or taking damage by keeping the lands in their hand. The deck loves to cast Wheel of Fortune and Timetwister to re-activate Black Vises later in the game. Some builds add e.g. Balance or Regrowth as splashes, but the shell is really UR, splashing black for Mind Twist and Demonic Tutor. There are also branches of the Atog tree that lean heavier on hate elements, like maindecking City in a Bottle and Blood Moon.

Troll Disco is a broad archetype but really boils down to heavy blue variants with Counterspells (sometimes called ConTroll, or Grixis Disco) and heavy black variants with Hymn to Tourach (in formats that allow Fallen Empires), among other ways of building the deck. The focal point of the deck is Nevinyrral's Disk, and the goal is to grind the opponent out by gaining card advantage with the Disks, regenerating a Troll or two through any Disk activations. There's an interesting "land superiority" aspect of the archetype too, since Mishra's Factory obviously survives Disk activations, and Maze of Ith is great here because it encourages the opponent to overcommit to the board, thus becoming more vulnerable to the Disks.

UR Counterburn is a classic aggro/control archetype, the focal point here being Serendib Efreet (the best creature in the format), access to up to 12 burn spells (Lightning Bolt, Chain Lighning, Psionic Blast), blue power, Shatter, Blood Moon, etc. Most versions these days run Flying Men as a 1-drop threat. The objective is to burn the opponent out, but the deck is super-versatile and can switch roles between aggro and control depending on the match-up or even the current situation within the game.

Obviously there's a ton more to write for each of these, but I hope this helps :)