Oath uses Oath of Druids to find large creatures with unwieldy casting costs and put them into play. The deck existed in the format ever since Oath of Druids was originally printed, however, it traditionally had difficulty getting Oath to trigger against decks that didn't play a large number of creatures. This drawback was largely erased with the printing of Forbidden Orchard, which not only improved the deck's mana base but also gave it an efficient way to give the opponent small creatures.
Early versions of the deck after the printing of Forbidden Orchard included Darksteel Colossus. Colossus has since given way to smaller creatures with haste. The "standard" first choice for most Oath decks is Akroma, Angel of Wrath, with either Spirit of the Night or Razia, Boros Archangel used as a backup depending on local metagames. However, due to the restriction of Brainstorm, Oath has suffered, due to not only the ability to draw three cards for one blue mana, but Brainstorm also allowed the player to efficiently put any creatures that they have drawn back into their library.
Another variant uses Serra Avatar, Fling, Berserk, Diamond Valley, and Altar of Dementia to quickly gain life and to boost the Serra Avatar towards a devastating Fling or Berserk.
Gaea's Blessing was nearly always included in the deck to prevent it from running out of cards, as its triggered ability reshuffles the owner's graveyard into his or her library whenever Oath of Druids happens by it.
The rest of the deck is typically devoted to countermagic with Force of Will and Mana Drain. It used to include card drawing and a small amount of removal, often in White (Swords to Plowshares and Seal of Cleansing).
As for the power-level errata on Time Vault almost every deck squeezes it and Voltaic Key as well as sometimes Tezzeret the Seeker for a two-card combo that instantly wins the game. Since its printing Iona, Shield of Emeria has become the supreme creature to cheat into play. Its ability turns off your opponent's ability to play their powerful spells as well as any removal they may have and can win with 3 attacks. Jace, the Mind Sculptor has become one of the most represented cards in Vintage printed in the last several years. Spell Pierce has become the counter magic of choice alongside Force of Will and Mana Drain as it counters nearly every spell in Vintage and costs only one blue mana.
Recently, creatures have been printed that far outclass old targets, such as Akroma. Emrakul, the Aeons Torn and Blightsteel Colossus combo with Dragon Breath in Golden Gun Oath. Iona, Shield of Emeria and Terastodon make up Elephant Oath. An older build that uses Tidespout Tyrant continues to see play in a combo deck known as Tyrant Oath. Some exotic builds even use Sun Titan to control the game post-Oath with Pernicious Deed or Chalice of the Void.
A typical Elephant Oath deck as of August 2010: