Most of the Greek gods of Mount Olympus looked like Greek gods, except Hephaestus and possibly Dionysus. In one myth, Hera threw baby Hephaestus off the mountain and left the god crippled. One theory, about the blacksmith god, says the god’s ailment reflects the afflictions dealt to bronze age blacksmith’s who used arsenic. Hephaestus also has some ties to Ptah, the Egyptian god, who is considered a dwarf. Egyptians had the popular dwarf god, Bes, and his lesser known other half, Beset.
The Norse gods often sacrifice a body part, but the loss often comes with significant gain. Odin loses an eye, but the loss gave him the ability to see all. Tyr, the Norse god of war and justice, sacrifices his arm when he binds Fenrir. Heimdall,the guardian, has only one ear.
There are several drunken gods and this is why I said he may not look like a Greek god, he likely staggers. Enki, the Sumerian god of creation, drank too much and Inanna seduced him. Obatala, an African deity who was brought to Latin America, is another drunken creator god, and his drunkenness led to people being born with deformities; which, led him to be the protector of those afflicted with deformity.
Attis, Uranus, Adonis, Dionysus, Set, Osiris, and most likely others lose their testicles or their penis; which, probably is metaphorical for seeding the earth.
Hiruko, a Japanese god of fishermen and one of the 7 gods of luck, is another dwarf.
Wikipedia says Xolotl was the Aztec god of fire and lightning. He was also god of twins, monsters, misfortune, sickness, and deformities. Xolotl is a dog, and I’m not going to list all the animal-styled deities, but he seem appropriate because of his link to monstrosities.
Here’s a quote from Wikipedia about another god of deformity, who may or may not be deformed: In Māori mythology, Punga is a supernatural being, the ancestor of sharks, lizards, rays, and all deformed, ugly things. All ugly and strange animals are Punga’s children. Hence the saying Te aitanga a Punga (the offspring of Punga) used to describe an ugly person.
Yoruba’s Lord of the Earth is said to be a leper who walks on crutches, but heals all, even impoverishment.
Papa Legba, from Haitian Vodou, like many tricksters sometimes limps.
Hawaii has 2 hunchbacks Kane-Hekili, spirit of the thunder and Ke-ō-ahi-kama-kaua, the spirit of lava fountains.
Southwestern Native Americans also have a hunchbacked deity–Kokopeli, the fertility deity, who plays the flute.
Tezcatlipoca used his foot as bait and Cipactli ( a monstrous crocodile) ate it.
Various deities related to the Cabeiri are dwarfs and Norse have many dwarves.
Sedna, the Inuit sea-goddess, lost her fingers which became seals and whales.
Priapus has a monstrous penis, so he may fit on this list.
I’m sure there are more, but that’s all for now.