This card can be Xyz Summoned with the effect of "Rescue Rabbit" by banishing itself to search for two Level 3 Normal Monsters. Since it's banished, it can be Special Summoned through this card and use its effect again next turn.
Or use "Macro Cosmos" to your advantage and Special Summon the Xyz Material that was just banished.
Keep in mind that this card can Special Summon from either player's Banished Zones.
In your own Macros Deck, use the following strategy to Summon "Gren Maju Da Eiza": Use "Tour Guide From the Underworld" to Special Summon "Da Eiza", and use both to Summon this card. Use this card's effect, detaching "Da Eiza" to Summon a monster, which banishes "Da Eiza". Then, on the next turn, detach "Tour Guide" to use the effect again and Summon "Da Eiza". (It is also possible to Summon directly "Da Eiza" by detaching it for the cost, and then targeting it for the effect of "Leviair")
"Skull Lair" can be used to banish your own monsters for this card's effect.
Use this card in a "RFG Psychic" Deck. Summon 2 Level 3 monsters with "Overdrive Teleporter", and Xyz Summon this card. Remove an Xyz Material to bring back either "Esper Girl" or "Mental Seeker" to use their effects.
In a Deck running the Plant Synchro engine, Summon "Leviair", then banish "Lonefire Blossom" for the effect of "Spore". Use the effect of "Leviair" to Special Summon "Lonefire" to the field, then Tribute "Lonefire" to Summon a Plant-Type monster of your choice from your Deck.
Use the "Mystical Shine Ball" that was returned to your hand with "Herald of Orange Light" or Summon it directly back to the field with "Venus". Using the effect of "Leviair", retrieve one of your banished Tuners (possibly "Earth" due to the Summoning condition of "Hyperion") to Synchro Summon using the remaining "Mystical Shine Ball".
Use this card with "Nordics" to bring back Tuner monsters banished for "Aesir" resurrection and Synchro Summon with them, allowing them to be reused to revive "Aesir".
Use this card's effect to Summon "Blue-Blooded Oni", which can be banished via "Allure of Darkness" or other means. Then use the effect of "Blue-Blooded Oni" to Summon a Level 4 Zombie from your Graveyard, allowing the Summon of a Rank 4 monster.
If "Leviair" is Summoned using "Tour Guide from the Underworld", this can get 2 Xyz Monsters off 1 card in hand.
Combine this card's effect with "Gold Sarcophagus" to bring the selected banished monster to the field rather waiting till your 2nd Standby phase to be in your hand.
The effect of this card can be used when a "Dragon Ruler" monster is used. When the "Dragon Ruler" Dragon is Special Summon, "Leviair" can be Summoned, and then use its effect to bring banished monsters to the field.