First, let's start by asking what is a curse? Curses are more serious than hexes, and can live on for generations if intended. They’re born of anger, hatred, or justice. However, curses can often be undone, in most cases, by the caster or target. Not feeling up for the long term punishment? Try a hex.
Poseidon is the God of the sea, earthquakes, soil, storms, and horses. His Roman form is Neptune. Poseidon lives on Mount Olympus or in the sea, depending on which myth you read. He was part of the 12 Olympians and also considered one of a smaller group called "The Big Three," which consisted of him, Zeus, and Hades. Poseidon's wife is Amphitrite, a sea Goddess, but he was constantly fooling around with other women, including Aphrodite and Demeter. He had many children, most of them being great heroes in Greek lore. These children include Theseus, Triton, Polyphemus, Orion, Belus, Agenor, Neleus, and Atlas. His parents are Cronus and Rhea, while his siblings are Hades, Demeter, Hestia, Hera, Zeus, and Chiron.
Zeus is probably the most well known of all the Gods. He is the God of the sky, lightning, thunder, law, order, justice, and eternal fire. He is the King of the Gods, and married his sister Hera. Zeus's parents are Cronus and Rhea. His siblings are Hestia, Hades, Hera, Poseidon, Demeter, and Chiron. His Roman form is Jupiter.
Tyche is the Goddess of luck, wealth, fortune, fate, and chance. Her Roman form is Fortuna. Her parents were said to be Aphrodite and Zeus, or Aphrodite and Hermes. She was said to be a companion of Nemesis and Agathos Daimon. The three gave out luck and fortune, as well as took it away, when punishment needed to be dealt out. Tyche was often the guardian spirit of the city's fortune and prosperity, and would be depicted with a crown shaped like the city's walls. Her statues would vary depending on the city, with either a stock of wheat, stepping on a swimmer, or with a cornucopia.
Hephaestus is the God of fire, metalworking, stone masonry, forges, and the art of sculptures. His Roman form is Vulcan. Hephaestus's parents are Hera and Zeus, but some myths claim it was just Hera alone. His wife is Aphrodite, although she is known to be unfaithful. He has many children including Thalia, Eucleia, Eupheme, Philophrosyne, Cabeiri, and Euthenia. Hephaestus is one of the 12 Olympians.
Eris is the Goddess of chaos, strife, and discord. Her Roman form is Discordia. There are many variants on who her parents might be. Some say it was just Nyx who gave birth to her, while others claim it was Nyx and Erebus. Some still think it was Zeus and Hera. She had many children, mainly thought to be Dysnomia, Atë, Lethe, Limos, Algos, Hysminai, Makhai, Phonoi, Androktasiai, Neikea, Pseudea, Logoi, Amphilogiai, and Horkos.