When Set, Stoke increases its Adept's base HP by 9, base Psynergy Points by 3, and base Attack by 3.
When Stoke is unleashed in battle, all currently active and alive Adepts get buffed with a 25% temporary increase to their respective attack ratings. This is twice as strong as High Impact/Angel Spear. All attack-boosting effects come in the form of 12.5% "stages", so therefore Stoke boosts each Adept's attack rating by 2 stages, and the maximum amount of stages an Adept's attack can be boosted to is 4, at +50%.
In Dark Dawn, Stoke's unleash animation visually resembles the user summoning the 3D model of Stoke above the party. It floats above the party while a small collection of purple and red orbs gathered into each currently-active Adept in order, and right after these orbs gather into an Adept, a pinkish-purple effect swirls from the ground into that Adept while a purple Sword image flashes in front of him or her briefly to indicate an attack boost.
Golden Sun: Dark Dawn: Stoke is automatically acquired in a cutscene later in the game, once the Grave Eclipse begins at Belinsk. When the game directs you to Belinsk's pier, follow along and board the sailing ship, and win the battle against three Gloom Skorpnas. In the story-relevant cutscenes that transpire after this, Eoleo permanently joins your party. He brings with him this Djinni along with four other Mars Djinn - Reflux, Wrath, Chili, and Glow.
General: The mass-attack-boosting effect that Stoke and other Djinn have is easily one of the best buffing effects in any of the games because the party's damage outputs with any action based on their physical attack statistics will be significantly increased, highly justifying the turn an Adept takes to cast it. Stoke is useful for the rest of the game it appears in once it is found. It is probably best to have it Set onto an Adept that has low attack rating and is dedicated to supporting the party to begin with, so that other, damage-dealing Adepts won't have to interrupt their attacking procedures in order to unleash Stoke.
Golden Sun: Dark Dawn: Stoke is basically a late-game copy of the highly useful Mars Djinni Forge found near the beginning of the game. While Forge has many, many more opportunities to be useful throughout the game than Stoke, Stoke is nonetheless beneficial to have late in the game. You may choose to have both of them Set onto one Adept, thus granting him or her the opportunity to cast the group-attack-buffing effect twice in subsequent turns, or have them Set onto different Adepts so that they can use the two Djinn separately at different times, perhaps even during the same turn. The mass attack-boosting effect shared between these two Djinn significantly increases the total damage of the whole party's physically-based offenses for several turns. As the boost to damage comes about from an increase to Attack rating, enemy Defense ratings end up being a less significant obstacle because they only decrease the damage of physical hits by a set value rather than some sort of percentage. This means that even Adepts that don't have high Attack, and score small amounts of damage when they physically hit certain enemies, will find the amount of damage they do with physical attacks to be much better than before, in relative terms. Since it boosts all four Adepts' Attack ratings, using it makes the Venus Djinni Chain, an attack based on the sum total of the physical hits of all currently-active party members, much more powerful than it already would be.