The first group consists of LIGHT Beast 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 LP 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 sizable 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" and "Teleia" can still be Special Summoned because they do so through their own effects.
"Theinen", the trump 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 its ATK to be boosted to by 3000 points during the turn it is Summoned. While this boosted ATK 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. It 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. The effect of "Theinen" allows either an greatly improved offense or an impenetrable defense (if it 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. The boosted ATK of "Theinen" is enough to destroy almost all monsters in the game, and as it can be Summoned from the Deck, as it 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, Master of The Guard" 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" 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 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.