Gigantic Formula

Kishin Taisen Gigantic Formula is a Japanese anime aired in 2007. The translation of the title is given as "Apo Mekhanes Theos Gigantic Formula".

Set in 2035, mankind had experienced a massive holocaust called the Equatorial Winter after 12 heads resembling Greek gods have been uncovered which ask for bodies with which to fight. The nations that have uncovered them, Japan, China, America, Russia, Italy, Germany, Britain, India, Egypt, France, Greece, and Venezuela engage in the "Wisest World War", governed by the United Nations, to unify the world under the rule of the victor.

Orphan Shingo Suwa earns the right to pilot Japan's Sxano-X (named after Susanoo) alongside Mana Kamishiro, one of the "translators" who can communicate with the stone heads.

Tropes used in Gigantic Formula include:

Action Girl - Mana and Kana are ninja.
After the End - the setting is after the Equatorial Winter which set the world on fire, literally.
Air Vent Passageway
All Your Powers Combined - Victorious Gigantics gain the abilities of those they defeat, and also the support of the defeated country.
American Robot - the North America Empire's Jupiter II.
BFS - a sword wielded by a Humongous Mecha is big by definition, and this one has trident-like attachments to make it bigger still.
Blush Sticker - well, the animation character designer did work on Kamichu!.
Combat by Champion
Conveniently an Orphan - None of the main child cast have parents.
Caped Mecha - the Jupiter II.
Captain Ersatz - Jupiter II kind of looks like Gallient.
Defeat Means Friendship - countries win the fealty of those they defeat, but team Japan actually does make friends with them, team China
Empathic Weapon
First Church of Mecha - while no worship is demonstrated, the Gigantics all contain the heads of ancient stone gods.
Humongous Mecha - of course.
Improbable Age - Ucchie, Sxano's Chief Engineer, is 10. Somewhat justified in that she is the product of Science.
Journey to the Center of the Mind / Mind Probe - the Psy-Harmonize system, which lets Mana and Shingo experience the memories of other pilots and translators. Could also be considered Mind Rape.
Latex Space Suit
Mind Rape - Russia's Hundred Eyes of Argus attack.
Named Weapons - The Sword of Murakumo.
Off-Model - the quality of some of the middle to late episodes slipped quite badly. While some actual errors were fixed for the DVDs, none of the shoddy work was re-animated.
Sentient Phlebotinum - the OXII.
Spell My Name with an "S" - Susanoo is written "Sxano" because it is Onyxs inverted.
Token Loli - Ucchie.
Toxic Phlebotinum - Pilots bodies' are gradually taken over by nerve cables. This happened to Sxano's first pilot and starts to happen to Shingo too.
Transforming Mecha - The Minervas-XI turns into a giant cannon.
Translator Microbes - while spying on memories via the Psy-harmonize system, they can understand what the foreign characters are saying.
Victor Gains Loser's Powers/Mecha Expansion Pack - Gigantics gain the abilities of those they defeat.
We Have Reserves - battles tend to start with conventional support forces being decimated.
X Meets Y - G Gundam meets Bokurano.