Hey! I'm KiritoShimura from NA server and I've been playing since s4. This galio build has been working pretty well for me(if you want check my ranked match history) and i just wanted to share it with fellow galio mains like myself. If you find a problem with my build please speak up and comment below :).
This build makes you tanky and lets you deal quite a lot of damage so please read and enjoy :).

In my opinion, when you are going the off-tank ap build, the W is the most essential ability after the Q. I know a lot of people like the maxxed out E over the W but tbh 35% reduced damage looks pretty good to me don't you think?
I usually just max Q then W then E in that order. ( I mean it always depends based on your build but since this is an off-tank build we are gonna go with max W second).

Pros

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+ AoE taunt and CC
+ Anti-mage champion
+ Big hitboxes, easy skill block
+ Near Global ulti that GIVES REDUCE DAMAGE
+ High base damages


Cons

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- Easy to dodge his skills
- Ad dps are strong against him
- His ganks are not irrepressible
- Doesn't have a reliable sustain

MARKS
Greater Mark of Magic Penetration: That pack of mark selections are viable for most tanky junglers and let you hurt enemies easier through your skills by a good amount, this is the best choice if not for Greater Mark of Armor, and is the best choice for mark slots.

Greater Mark of Armor: These allow you to dive easier and take less damage from per auto attack, as a tank taking less damage is great since dying is always a thing XD.

GLYPHS
Greater Glyph of Magic Resist: Have you ever noticed that galio's passive and w scale off of magic resist. Have you ever just killed someone with the passive boosted with an iceborn or lichbane? Well the MR plays a big roll in it and i know we all want to hulk smash a darius :). Almost every champion has a strong side, and some champions benefit more from a mere stat, and this stat of Galio is magic resistance, something similar to Vladimir's building hp and it becomes more ap for him.


SEALS

Greater Seal of Armor:These allow you to dive easier and take less damage from per auto attack, as a tank taking less damage is great since dying is always a thing XD.

Greater Seal of Scaling Armor: Scaling armor is also nice... just depends on your preferences :)

QUINTS

Greater Quintessence of Ability Power: As a mage/tank, flat ap is always viable for your rune choice, taking these instead of armour quints are also recommended too, but I'm usually taking armour quints because of awesome early tankyness. It allows us to build things like hp cdr in first priority.

Masteries are masteries... colossus and thunderlords are both viable, but the 18/12 build in the cunning/resolve areas respectively works the best for me. You choose whichever you prefer- damage or invulnerability