Most Exodia variants play all spell cards and are completely dependent on them. Something like Anti-Spell Fragrance, Imperial Order, or Eradicator Epidemic Virus will lock them down completely. You can also negate Spells with cards like Magic Jammer, Dark Bribe, and Cursed Seal of the Forbidden Spell.

How do you beat Exodia?

After resolving a Chain Link, if you have "Exodia the Forbidden One"/"Right Arm of the Forbidden One"/"Left Arm of the Forbidden One"/"Right Leg of the Forbidden One"/"Left Leg of the Forbidden One" in your hand, you immediately win the Duel.

What can destroy Exodia?

Exodia Cards

It gains 500 ATK during each of the player's Standby Phases and cannot be destroyed in battle or by Spell and Trap effects. It is automatically destroyed if any of the five "Forbidden One" pieces do not exist in the Graveyard.