A few general ideas:
The weakness of counterspell-heavy decks is dealing with all the important threats efficiently, and not tapping out prematurely. This is particularly tricky to pull off in multi-player, since controlling more than one player is much more work. On the receiving end, it might feel to you like he has a counterspell for everything, but that simply can't be the case. If the player to your left plays a couple of spells and gets countered, that makes it much more likely that you will be able to drop something safely into play.
One big limitation of creature removal is that it generally only works on creatures. An extreme way to screw with a powerful creature-controlling deck is to not field any creatures! Try direct damage, artifacts or enchantments instead. All of those kill spells become ineffective against your deck, and the resulting hand of dead cards can be crippling for your opponent.
An intermediate approach is to pick creatures that are exceptionally hard to kill. Your choices are many, and depend on the kind of spells your opponent uses most. Against powerful sorceries like Wrath of God, you could consider creatures that revert to some other type at end of turn (e.g. Mishra's Factory, Genju of the Realm), or ways to generate endless hordes of cheap tokens (Assemble the Legion, Kjeldoran Outpost), or just bounce with unbelievable annoyance (Blinking Spirit). Against direct removal, protection or regeneration can be extremely annoying. Or just pick creatures that either like going to the graveyard (Demigod of Revenge), or can easily come back (e.g. Ashen Ghoul, Pyre Zombie, any of the Phoenixes).
Another approach is to accept that your stuff is going to end up in the graveyard, and use that to your advantage. Returning creatures from the graveyard can be very efficient, or you can use a large graveyard to power effects like Threshold, or to give you access to spells that can be cast from the graveyard (e.g. anything with Flashback). Or make filling the graveyard your win condition (Mortal Combat, Nefarious Lich).
A more aggresive idea is land destruction/mana control. You probably won't win your multi-player game, but you could easily make it impossible for this particular opponent to win. In a similar vein, you could go for counterspell/control yourself, and shutdown his nastiest spells to let the other players do their thing.
A final tactic is to make yourself an unappealing target. Don't be a threat, sit there and protect yourself, while building towards some late game win condition (Door to Nothingness, Test of Endurance).
Above all, stay positive, and be creative! You have many, many pleasant options for ruining your opponent's game.