"Volcanic Eruption" is not a "Volcanic" card because it does not have 「ヴォルカニック」 in its Japanese name.
Both Volcanic Slicer and Volcanic Doomfire appear as characters in Yu-Gi-Oh! World Championship 2008, and Volcanic Shell appears in Yu-Gi-Oh! 5D's World Championship 2010: Reverse of Arcadia.
Most of the "Volcanics" are reptilian, combined with military hardware and are intended to be used with the card "Blaze Accelerator", which destroys opposing monsters by using Pyro monsters as "ammunition" by sending them from your hand to the Graveyard.
The main theme of the "Volcanic" archetype is working in conjunction with the "Blaze Accelerator" cards, inflicting massive effect damage over time while also steadily destroying the opponent’s board. As a result, monsters such as "Volcanic Scattershot" and "Volcanic Shell" are staples within the deck, as they allow for both mass-destruction and regaining hand advantage respectively. However, the downside of this play-style means often giving up your Battle Phase in return. Despite this however, some members sport relatively high ATK values; one such card is "Volcanic Rocket", which can search out any of the "Blaze Accelerator" cards upon Summon while providing a good 1900 body, making it essential in any build. Higher Level members like "Volcanic Hammerer" sport a healthy 2400 for a Level 5 monster with a chance to inflict healthy amounts of damage, as each "Volcanic" monster in your GY becomes 200 points of damage. With at least 6 copies of both "Shell" and "Scattershot", this can go from a mere 1200 to potentially high enough to end the game after a while. "Volcanic Slicer" provides a lesser version of this effect as only inflicts a fixed 500, making it not really worth running. Meanwhile, "Volcanic Counter" is arguably one of the best members, giving immediate retaliation to any battle damage taken by throwing an equal amount right back; the only downside is that due to the effect being mandatory the opponent can easily bait this out. Interestingly, one of the boss monsters - "Volcanic Queen" - acts somewhat similar to a "Kaiju" monster, Tributing a monster the opponent controls to Special Summon itself to their field and can burn the opponent for 1000 damage each of their End Phases unless they’re able to Tribute another monster. But be warned as they can still use the effect of "Queen" to inflict 1000 damage to you in return. "Volcanic Doomfire" on the other hand, as the "king" to "Queen", is much more battle-orientated as it forces the opponent to ram their monsters into it provided they’re in Attack Position which can lead to a full-on monster-nuke on top of 500 per monster destroyed. Note that to Summon "Doomfire" one must give-up a copy of "Tri-Blaze Accelerator", so one may want to be careful in deciding when to use it.
As one may guess, "Blaze Accelerator" cards are must, with each one providing benefits such as "Blaze Accelerator Reload" giving you draw power. "Volcanic Recharge" can help prevent running out of ammo for your play-style. If mixing in any FIRE monsters with 200 DEF, you can run "Flamvell Counter" protect yourself from any opposing Spell/Traps.
"Royal Firestorm Guards" is extremely useful within the deck, not only recycling 4 of your monsters in the GY but providing a draw-2 when Summoned. "Paleozoic" monsters such as "Paleozoic Leanchoilia" and "Paleozoic Marrella" can aid in this strategy allowing you to recycle and mill out your reload quicker. "Lava Golem" also fits in perfectly with the "Volcanic" play-style. Alongside "Queen" this can quickly bring your opponent to being obliterated by "Hammerer", as can "Solar Flare Dragon" which provide a maximum of 1500 damage during your End Phases per copy of itself present.