I feel very bad for how good this deck is. While I've tried many other Exodia recipes (always around the free/budget card range), this one is the most effective (unluckily).
While there are many Exodia cards in the archetype, the most common winning condition is to try and gather all 5 pieces to hand. Most decks are using legal and illegal cards to succeed, but this deck is different.
This deck is trying to special summon "Crooked Cook" while one of it's materials has to be "Right-Hand Shark" or "Astral Kuriboh". This way if it's the only card on your field it cannot be affected by other cards or destroyed by battle. So basically you just have to wait every turn patiently and passively, till you draw all the pieces. Be ware, that you might have to wait for more than 40 turns by doing nothing more than discarding cards from hand at the end of your turns and NOTHING ELSE.
Try not to discard "Right-Hand Shark" or "Astral Kuriboh" if possible cause "Called by the grave" might be enough to negate your "Crooked Cook's" protection.
On the other hand cards like, Kaijus or other cards that can use YOUR monsters as materials can remove Crooked Cook from the field.
Some even more weaknesses of Crooked Cook are: Penetration, Direct attacks, Burn decks
While some other weaknesses of this Exodia deck are: Deck/Hand destruction/banish (Kashtira and Runick decks).
All of these things can really lose you games, but not all duelists are prepared for Crooked Cook.
As I was playing with this deck I've found that it's most common to win by decking-out your opponent than drawing 5 pieces of Exodia (LOL). Which doesn't feels right but at least you have 2 winning conditions.
12 of the cards are here to summon Crooked Cook, 5 of them are Exodia pieces, 14 of them skip battle phases and all the other, are cards to disrupt opponent's combos or board breakers.
You can run a second Crooked Cook as I did, but you can still play the cheap way with only one.