Take that Exodia!!___ Mr. X
If you can't win against Exodia decks or just don't like Exodia decks, perhaps using some underlooked cards might work. All you have to do is have some of these cards while facing an Exodia Deck:
Disappear
Trap
SYE/LOD
Select 1 card from your opponent's Graveyard and remove it from play.
*Simply chain this card to their Back Up Soldiers.
Respect Play
Continous Trap
PSV/DB1
During their respective turns, each player must show their opponent their hand.
*Sure, you show them your hand, but let's not focus on that.
D. D. Designator
Spell
IOC
Declare 1 card name. Look at your opponent's hand, and if he/she has the declared card in his/her hand, remove that 1 card from play. If he/she doesn't have the declared card in his/her hand, remove 1 random card in your hand from play.
*Now, if you have the Respectful Play on the field, you'll know what they have. If they have a piece, then simply remove it. Just call the right piece ^_^
Some unrealistic/weird combos with these cards that are not widely played, but hey, it doesn't hurt to try.
-Mr. X