Angelic weapons are implements belonging to Heaven that are imbued with some supernatural power. The most common is the angel sword. Following the imprisonment of Michael and Lucifer in Lucifer's Cage, a civil war takes place in Heaven. A collection of powerful weapons from Heaven's armory disappear, and are then sought by rival factions of angels.
Castiel: Before the Apocalypse, Heaven may have been corrupt, but it was stable. The staff was safely contained. It's been chaos up there since the war ended. In that confusion, a number of powerful weapons were stolen.
Dean: Wait, you -- you're saying your nukes are loose?Castiel: Yeah, I'm afraid so.
In the battle between angels to control Heaven, Castiel says "Whoever has the weapons wins the war." Raphael wants the weapons so he can take control of Heaven and restart the Apocalypse. It is discovered that Balthazar stole the weapons, and wants them for his own unstated ends. He uses a portion of one weapon to buy a human soul, and destroys Raphael's first vessel with another. Eventually Balthazar decides to turn the weapons over to Castiel. Castiel confirms to Raphael at their next confrontation that he has the weapons, which forces Raphael to flee.
At first, it seemed that the "Sword of Michael" was an actual angelic weapon which Michael used to defeat Lucifer, but it is later revealed by Zachariah that Dean Winchester is in fact the "Michael's Sword" - Michael's true vessel.
This short, silver blade can wound and kill angels. Multiple blades exist, and by season five most angels carry them. It has been shown that humans and demons are capable of effectively wielding them as well and they are deadly to angels, demons, hellhounds, reapers and Nephilim.
Longer sword version of the angel blade.
This crystal turns a human body to salt.
When people start being compelled to tell the truth, Dean and Castiel suspect that it made be caused by Gabriel's Horn of Truth. However the Horn is not found in the city, and the culprit is revealed to be the goddess Veritas.
Castiel tells Sam and Dean there is a weapon that will kill Fate. Balthazar appears behind Atropos with a blade but Castiel stays his hand. The weapon appears similar to an angel sword although the blade is more rapier-like in shape, and it is golden in color.