I downloaded a ghost of this player on WC 2008. He was on the top scoring list, so I wanted a challenge.
I can't beat him though, because in all the three duels I had, he/she plays Exodia in the first or second turn.
Is there any strategy to this, or is it a plain cheat? >.<

LOL Either he was able to get all his pieces by using good spells or he got it on the first draw. XD However, I think it is possible with cards that add spellcasters to your hand, which does work.

I really want to know what spell card he uses to get all the Exodia cards on the first draw.

First draw must be luck only, unless he got two pieces, used foolish buriel twice and then got them with dark eruption.

If you got Heart of the Underdog then pulling Exodia isn't a null idea, just make sure you balance it correctly, and you can pull Exodia within a few turns.

Draw power, basically just keep drawing and adding until you get all the pieces.

Hmm... well its not impossible to run a deck where you can draw all 5 parts in one or two turns. I myself have a blue-eyes exodia hybrid that draws it (also known as dragons draw) which abuses the two draw cards (one for tuners, and one for level 8 monsters) including toon table of contens for toon blue eyes, and super reguvination. So with that deck you can pull exodia first turn easy. However as for fighting it... I can think of one sure fire way (almost) most decks that focus on that strategy don't put in anyways of defending from anything (thinking they will win automatically) so you should try the card "Protector of the Sanctuary".

http://yugioh.wikia.com/wiki/Protector_of_the_Sanctuary

Its a VERY old card but effective against any kind of exodia based deck.

That's why I think that no decks are foolproof. There will be someone who can beat it since they have the weakness of the deck. This being one of them.