Discordia: Also Discord, Eris (Greek). Goddess of discord and strife. Daughter of Zeus and Hera; twin of Ares. Sister of Fear, Panic, Terror, and Trembling, the four sons of Ares [how could she be both their sister and their aunt?]. Famous for roApple of Discord across the floor at the wedding of Peleus and Thetis. This apple, marked For the Fairest, was claimed by three goddesses--Aphrodite, Athena, and Hera. It led to the Judgement of Paris and indirectly to the Trojan War.
Eris: see DISCORDIA.
Strife: A son of Eris. Eris (Roman:Discordia) is also called Strife, or the goddess of discord and strife.
Source: Zimmerman, J.E. Dictionary of Classical Mythology. Bantam Books: New York, 1971. pp. 88, 98, 248

Discordia: NO LISTING
Eris: The personification of Strife. In Hesiod's Theogony she is a daughter of NYX and herself gives birth to Work, Forgettfulness, Hunger, Pain, Battles, Fights, Murders, Killings, Quarrels, Lies, Stories, Disputes, Lawlessness, Ruin and the Oat. In the Works and Days, Hesiod postulates two seperate Strifes: one a daughter of Nyx, the other a spirit of emulation, placed by Zeus within the world to give it a healthy sense of competition. Eris was generally portrayed as a female winged spirit. She threw the apple intended for the fairest of the goddesses, which PARIS had the task of awarding; this was the origin of the Trojan War.
Strife: NO LISTING
Source: Grimal, Pierre. Dictionary of Classical Mythology. Penguin: New York, 1991. pp. 142-143,

Discordia: The personified Roman goddess of strife and discord. She belonged to the retinue of Mars and Bellona. She is the Greek Eris.
Eris: Eris is the Greek goddess of discord and strife. She is Ares' constant companion and follows him everywhere. Eris is sinister and mean, and her greatest joy is to make trouble. She has a golden apple that is so bright and shiny everybody wants to have it. When she throws it among friends, their friendship come to a rapid end. When she throws it among enemies, war breaks out, for the golden apple of Eris is the Apple of Discord. She did this once during the wedding of Peleus and Thetis, and this act brought about the Trojan War.
Strife: NO LISTING
Source: Encyclopedia Mythica

Discordia: NO LISTING
Eris: Known to the Romans as Discordia, it is from this name that we get a clue to this goddess's nature. Goddess of strife, she was employed by the other gods to stir up fierce disputes and mortal quarrels among men. It was she, in fact, who started the quarrel among the three goddesses, Hera, Athene and Aphrodite, at the marriage of Peleus. She lived in the lower world with the Erinys, and was at times represented as the wife or sister of Ares. She was mother to Enyo, goddess of war.
Strife: NO LISTING
Source: Of Gods and Men: The A to Z of Mythology and Legend

Discordia: Discordia was the Roman goddess of strife.
Eris: Eris was the Greek goddess of strife, deceit, discord and disputation. The provoker of rivalry, contention, murder and wars.
Strife: NO LISTING
Source: The Probert Encyclopaedia of Mythology

Discordia: NO LISTING
Eris: Eris is the goddess of discord and the spirit of strife, and the daughter of Zeus and Hera. She is obsessed with bloodshed, havoc, and suffering. She calls forth war and her brother Ares carries out the action. She had a golden apple that was so bright and shiny everybody wanted to have it. When she threw it among friends, their friendship came to a rapid end. When she threw it among enemies, war broke out, for the golden apple of Eris was an apple of discord.
Strife: NO LISTING
Source: Luminara's Web of Myth-tery

Discordia: NO LISTING
Eris: Eris is the personification of Strife. She is portrayed as an ugly old woman.
Source: Perseus Encyclopedia

Discordia: NO LISTING (thought to be the same as Eris)
Eris: "Eris is Discord, and may be called strife and quarrel as well." She is considered to be either the daughter of Nyx or the sister of Ares. She is a goddess to fear, as her powers are great and many, and she is often portrayed as having wings.
Source: Greek Mythology Link