This is a deck for Yu-Gi-Oh! 5DS's World Championship 2011: Over the Nexus. You can summon Exodia turn 1, but if you can't do that, you might still be able to fight back like a normal deck.
The main draw engines are Tuningware De-synchro (Ideally 3 draws per de-synchro, 2 if you use it on Formula Synchron, or, in the worst case, 1. And when you run out of De-Synchro, instead of making a 3 draw synchro summon if possible, i recommend to get up to 6 draws by summoning Formula Synchron instead), Royal Magical Library and Bamboo Sword. Cup of Ace is there too if you're lucky enough.
In this game Brionac is Pre-errata, and for some reason Dark End Dragon doesn't target.
If you prefer it to be 40 card and oriented towards a first turn win, move Malicious to the side, this way it's more consistent on setting up the draw engines but considerably weaker when you either brick or can't recover all pieces of Exodia.
When it comes to dueling, you can summon 2 Shooting Star Dragon with a 5 card combo (if you draw Monster reborn with the draws you get along the way + after), or De-Synchro Mistwurm to clear a field, equip Armory Arm to a Synchro, use De-Synchro on your opponent, etc.
Malicious doubles as discard fooder/Foolish target and a LV7/8 Synchro material (with it you can summon two Shooting Star Dragon with a 5 card combo). It's also good as not to run out of Foolish Burial targets.
Remember not to de-synchro your monsters if the materials are no longer in the GY (careful with Plaguespreader Zombie)
If you brick and discard the head of Exodia, make sure to save Monster reborn to summon it and bring it back to hand with Zephyros (who can also be used for synchro summoning, to get more discard fooder and for an extra spell activation. Remember that in Tag Duels both you and your partner can use it's effect. If you prefer Monster Reincarnation replace it).
If you can't recover all pieces of Exodia, focus on dueling.
If you have to end your turn and had activated Into the Void, set your spells beforehand. If you have Plaguespreader in GY, you might also be able to save a card from being discarded.
I know Pot of Avarice is a weird pick for a Exodia deck, but it can give a second chance to use Machine Duplication and/or Royal Library, and that is a chance to end the duel in the same turn.
If you don't like Cup of Ace, i left an alternative on the side deck. And if you want more discard fooder, Thunder Dragon is there too.