Infernity Guardian is a monster that was created as a promo card in the World Championship DS series. Lucky for me, I acquired one of these back in 2009. This card is part of the "Infernity" Archetype, which bases its strategy using zero cards in the hand. This cards effect states: While you have no cards in your hand, this face-up card cannot be destroyed by battle or by card effects. In simplified terms, a brick wall.
The main use of this card is to stall your opponent in order to give yourself a few turns to set up. This isn't a beat stick, so I'd advise using it for stalling purposes only.
Strategies and game play:
This card is best used when it is special summoned to the field, so that you can put it into face-up defense mode. Great ways to do this are using cards like Infernity launcher. (You should special summon in defense mode to avoid battle damage)
or Infernity Necromancer
Combos with other cards:
Remember, this card only works when you have no cards in your hand. One way to get rid of your hand is to use cards like Infernity Inferno
One card I found that can really benefit you is to use Torrential Tribute. Infernity Guardian
will remain on the field, while your opponent's monsters burn! ('')
Ways to counteract it: (aka the weakness)
Though this card seems almost impossible to run over, there are a few ways to get rid of it. One way is to remove this card from play (removing from play isn't considered "destruction"). For example, BLS can remove this card with his effect
Another easy way to remove Mr. invincible, is by using one of the best trap cards in the game. This trap can also deal with Synchros and Xyz monsters without a problem. This card is called Compulsory evacuation device. This card returns a monster to the hand.
One more way to deal with this card is to flip it face-down, thus negating the effect. Book of Moon will usually deal with this.
This card is about a 9/10 in my book. It usually is reliable for the turns I need to set up a new move.