"Evigishki" (or just "Gishki" on certain cards), known as "Eviritua" (イビリチュア Ibirichua) in Japan, is a series mainly composed of WATER Ritual Monsters (and, more recently, Xyz Monsters too) that is part of the "Gishki" archetype. They are Ritual Summoned using one of the numerous "Gishki" Ritual Spell Cards, most prominently "Gishki Aquamirror". They receive implicit support from "Gishki" support cards, but have no true support cards of their own.
All "Evigishki" monsters are corrupted, transformed or even combined versions of pre-existing "Gishki" monsters with each other or with monsters from another archetype or a monster from another archetype that was transformed/revived as an "Evigishki".
The Levels and ATKs of the "Evigishki" Ritual Monsters cover a wide range, from Level 4 and 2150 ATK with "Gishki Psychelone" all the way up to Level 10 with 3200 ATK with "Gishki Zielgigas". Their effects primarily focus on controlling where cards are located, taking away options from your opponent and making it harder for them to get those options back while giving you much easier access to your own. Some, like "Evigishki Gustkraken", only work upon being Ritual Summoned, while others, like "Evigishki Tetrogre", can be used turn after turn.
Despite the wide variety of Levels of these Ritual Monsters, performing their Ritual Summons can be achieved with a single Tribute by using either "Gishki Shadow" or "Gishki Vision", which both possess an effect that allows them to cover the entire cost of the Ritual Summon by themselves, as well as being able to search out the required Ritual Spell and Ritual Monster, respectively.
"Evigishki Merrowgeist" is an Xyz Monster and, so far, the only one non-Ritual Monster of the "Evigishki" series. It can be easily Xyz Summoned by using the effect of "Gishki Beast" and is very useful against monsters that activate their effects by being sent from the Field to the Graveyard: by detaching one of its Xyz Materials after Damage Calculation, you can shuffle that monster back into the Deck, a strategy that follows the standard game-play of the "Gishki" Archetype.
Though "Gishki Zielgigas" and "Gishki Psychelone" don't have the prefix "Evi-" in their English names, both have "イビ-" in their Japanese names and are thus included in this series.