"Andro Sphinx" and "Sphinx Teleia".
The first group consists of LIGHT-Attribute, Beast-Type monsters. These are "Andro Sphinx", "Sphinx Teleia" and "Theinen the Great Sphinx". They were released in an exclusive pack after the release of Yu-Gi-Oh! The Movie: Pyramid of Light.
"Pyramid of Light" allows Andro and Teleia to be Special Summoned at a cost of 500 Life Points each, creating strong beat-sticks for no tribute. While they can't attack the turn they are Summoned, they are strong enough to weather most attacks and survive until they can. Their effects allow them to inflict additional damage as well as that incurred by their sizeable ATK points. These monsters cannot be Special Summoned from the Graveyard, so you will need to stop them from getting destroyed by your opponent's card effect (for instance by using the effect of "Stardust Dragon") or, if they are destroyed, return them to your hand using "Monster Reincarnation". You can also Normal Summon these two monsters, so Pyramid of Light is not essential.
The reliance that these monsters have on "Pyramid of Light" can be a disadvantage: it can be easily destroyed, especially with cards like "Mystical Space Typhoon" or "Nobleman of Extermination", which can banish all three copies at once. However, even if cards like "Jinzo" or "Royal Decree" negate "Pyramid of Light", "Andro Sphinx" and "Sphinx Teleia" can still be Special Summoned because they do so through their own effects.
"Theinen", the Triumph card, can be Summoned only by paying 500 Life Points when "Andro" and "Teleia" are destroyed at the same time, making him a useful backup if your opponent destroys your monsters with Dark Hole or destroys the "Pyramid of Light" should it be on the field. His effect allows his ATK to be boosted to by 3000 points during the turn he is Summoned. While this boosted attack is not enough to OTK the opponent, it is enough to either destroy most powerful monsters or wipe out most of the opponent's Life Points. He is, however, a Dead draw, so cards that bring out Andro, Teleia and the Pyramid of Light are helpful.
The effects of Andro and Teleia make them very powerful in offense. Not only do they have very high ATK points, but they inflict either half of a destroyed monster's DEF or ATK as additional damage. This is especially useful when they are used to destroy Defense-position monsters when no damage would normally be inflicted. Theinen's effect allows either an greatly improved offense or an impenetrable defense (if he is Summoned during your opponent's turn).
While the combined powers of Andro and Teleia are greater than that of Theinen - the two monsters are able to inflict much more damage together than Theinen can in most cases - Theinen is a useful tool to call upon should your opponent have an extremely high-powered monster (like "Malefic Rainbow Dragon") which the other "sphinx" cards cannot destroy. Theinen's boosted ATK is enough to destroy almost all monsters in the game, and as he can be Summoned from the Deck he does not have to be in the hand for you to use this option. This means it can be advisable to sacrifice the power of Andro and Teleia by destroying them yourself, either with Dark Hole or by destroying your own Pyramid of Light in order to bring out Theinen from the Deck.
They mainly enhance Deck which use the "Once per turn, you can flip this card into face-down Defense Position" effect. Though it has to be Tribute Summoned, "Hieracosphinx" prevents your face-down monsters from being attacked. "Criosphinx" forces your opponent to discard card(s) from his/her hand after the same number of monster(s) on his/her side of the field return to his/her hand. Therefore "Criosphinx" and "Guardian Sphinx" form a combination which can prevent your opponent from viably Summoning anything.
"Exxod" is not a "sphinx", but can only be Special Summoned by Tributing a "sphinx". "Exxod"combined with "Hierarcosphinx" makes a lethal force; every time an earth monster is Flip Summoned, "Exxod" inflicts 1000 points of direct damage to your opponents Life Points. With "Hierarcosphinx" on the field, your face-down cards cannot be attacked. The cards except "Hieracosphinx" are especially vulnerable to "Gaap the Divine Soldier" and "Final Attack Orders".
Also, "Dark Simorgh" and "Light of Intervention" can kill the effects of "Guardian Sphinx" and "Exxod, Master of the Guard" because a player will be unable to Set their monsters face-down, therefore monsters cannot be Flip Summoned.
"Clear World" seems like a good addition to this Deck, since cards in this Deck have the effect of being flipped face down, and face down cards cannot be targeted by "Clear World". However, the effect of "Clear World" for EARTH attribute monsters destroys a face-up defense position monster you control during your Standby Phase. Your opponent can take advantage of this, and attack your face down monsters, even if they know they cannot destroy them, because "Clear World" will