Individually, each "Invoked" represents a different Attribute, with their Fusion Materials being "Aleister the Invoker" plus one monster of their specific Attribute, and are named after historical or mythological elements related to said Attribute. They also contain the staff of "Aleister" somewhere in their artworks, but much brighter than the original.
Starting with either the Field Spell "Magical Meltdown" to search "Aleister the Invoker" who searches for this archetype's Fusion Spell card called "Invocation", this can Fusion Summon any monster using Materials from the hand, and can also banishFusion Materials from either GY or your field if Summoning one of the Invoked monsters. It can also recycle itself to the Deck and a banished "Aleister the Invoker" to your hand. Aleister can also act as a handtrap, giving any Fusion Monster +1000 ATK until the end of the turn.
This traits give the Invoked strategy a lot of versatility for many reasons. Firstly, they can access generic Fusion Monsters without needing Polymerisation or other off-archetype cards. Secondly, you only need one Aleister to produce an unending stream of Invoked monsters. Thirdly, the ability to banish monsters from either GY means you can deny your opponent a chance to recycle important monsters while possibly gaining an unusual Attribute for your Deck. Finally, the ability to banish other monsters from your GY means you can use your monsters on field for a Link/Synchro/other Fusion Summon, before getting a second use from them.
However, it is rare to see "pure" Invoked Decks, as there is not too many Main Deck components to this Deck, and Aleister is the only Main Deck monster, requiring other monsters to be played to access most of the Invoked monsters. As a result, Invoked are most commonly seen as an engine in other Decks, particularly those with little to no Normal Summon reliance, or that play Brilliant Fusion to get an extra Normal Summon. These Decks can give up the Normal Summon to Aleister while successfully executing their main strategy, using the Invoked to provide either offensive firepower or defence to help their plays go off. Examples of Decks that have use Invoked strongly include Windwitch and Mekk-Knights, while Thunder Dragons and Trickstars are modern meta decks that have experimented with this build.
The Invoked Fusion monsters are naturally not all viewed as equally strong, and choosing to play them often revolves around which you can Summon. Caliga, Magellanica and Cocytus are viewed as being comparatively weak, but they can still be viable especially if their Attribute is strong in the current meta, as their Summoning will often be far easier. Elysium is often viewed as practically infeasible to Summon, and as not giving enough rewards for the large investment made in it, so is nearly never played.
Invoked Raidjin is a highly versatile option that effectively provides a Book of Moon every turn. The fact it is a Warrior and can be Summoned off Instant Fusion also makes it popular in Decks that Summon Isolde, Two Tales of the Noble Knights. Invoked Purgatrio is a highly dangerous monster that gains ATK for each card your opponent controls and can attack all monsters your opponent controls. As it also does piercing damage, it can OTK the opponent in a flash, making for a startling contrast to the Deck's mainly more control focussed options. Finally, Invoked Mechaba has an awesome negation effect that can negate any effect in the game once per turn by discarding the same type of card as your opponent activated (Monster/Spell/Trap), and then banish whatever was on the receiving end of this effect. If you can Summon multiple Mechaba, your opponent will have a hard time doing anything if you have the right cards in hand.
With the release of Aleister the Invoker of Madness as a dedicated Link Monster for this archetype, Decks that play Invoked Monsters now can Fusion Summon even more often, and can even use the Invoker of Madness himself for a last Summon, as his name becomes Aleister the Invoker on the field. He also gives better support to the archetype's other non-Fusion Spell/Trap cards, so those may be worth considering more often now.
"Chain Disappearance" can be used to banish all copies of "Aleister" at the time it is Normal Summoned. Bear in mind, though, that if "Invocation" is sent to the Graveyard, by a card like "Twin Twisters", "Foolish Burial Goods", etc, those copies can be easily retrieved.
"Imperial Iron Wall" can be used to prevent the "Invoked" player from banishing monsters from their opponent's Graveyard, and can also disable the powerful effect of "Invoked Mechaba", since it will not be able to banish the card it would have negated.