My current Exodia deck is:
Monsters:
3 x Sangan
2 x Emissary of the Afterlife
3 x Right Leg of the Forbidden One
3 x Right Arm of the Forbidden One
3 x Left Leg of the Forbidden One
3 x Left Arm of the Forbidden One
3 x Exodia the Forbidden One
Spells:
3 x Graceful Charity
3 x Pot of Greed
3 x Upstart Goblin
3 x Dark Hole
3 x Swords of Revealing Light
3 x Pot of Duality
Traps:
2 x Jar of Greed
It's not optimal but it gets the job done. I'll probably replace the Emissaries with Witch of the Black Forest at some point. I completely forgot about that card until I saw the deck in your link running it.
Try skimming down to one copy of each Exodia piece, it cuts down on pointless draws (Multiples of Exodia you don't need for example)
Pot of Duality can only used for one turn and on that one turn only so having multiples of them on a single turn is just an extra card in your hand you cannot even use.
Replace it for Allure of Darkness instead. (Banish one dark monster and get two cards, since every monster in the deck I recommend is Dark it's basically getting two extra draws)
This is what I use.
1x Left Arm of the Forbidden One
1x Right Arm of the Forbidden One
1x Left Leg of the Forbidden One
1x Right Left of the of the Forbidden One
1x Exodia the Forbidden One
2x Makyura the Destructor = allows traps to be used on the turn it's sent to the graveyard. Also fuel for Allure of Darkness
2x Armageddon Knight = Allows you to send a Dark Monster to the Graveyard from your Deck, For Makyura's Effect, it's a Dark Monster so Allure of Darkness Fuel
3x Sangan = Dark Monster that when sent from the field to the graveyard to grab an Exodia Piece
3x Witch of the Black Forest = Dark Monster when sent to the field to the graveyard to grab an Exodia Piece
Traps / Spells
3x Pot of Greed = draw 2 cards
3x Graceful Charity = draw 3 cards, discard 2 cards
3x Jar of Greed = draw 1 card
2x Allure of Darkness = Draw 2 Cards Banish one Dark Monster (Sangan and Witch used as fuel for this effect)
3x Good Goblin Housekeeping = Draw 1 card times number of Good Goblin Housekeeping in your graveyard, send one card back to your deck.
3x Upstart Goblin = draw 1 card, opponent gains 1000 LP
2x Dark World Dealings = Draw one card, discard one card
3x Reckless Greed = draw 2 cards skip your draw phase
3x Legacy of Yata Garasu = draw 1 card
Basically the idea is the get Makyura into the Graveyard either by the effect of Armageddon Knight, Graceful Charity, or Dark World Dealings. And just never stop drawing cards until you have your 5 Exodia Pieces and win.
In the case you don't have any draw cards, and just have Sangan or Witch in your hand, put them down in defense mode, they get destroyed, you get a free Exodia piece. Generally a duel should end on first round, second round at worst.
Makyura's useful in that once he's sent to the graveyard you can then use Trap Cards as if they were like spells. So instantly using Reckless Greed, Jar of Greed, Legacy of Yata, and Good Goblin Housekeeping are just extra draw attempts to pull your deck out as quickly as possible and get your Exodia pieces into your hand.
