Underworld
The Underworld is the place of bad souls (this includes evil spirits and the souls of dead people who were cruel and evil in their lives) and the home of Ördög, creator of everything bad for humans: for example, annoying animals such as fleas, lice, and flies.

Csodaszarvas (White/Miracle Stag)

Álmos: Son of Ügyek and Emese. He was a semi-legendary figure born in c. 819 and the ancestor of the house of Árpád. Álmos ruled the Magyars in Levedia and Etelköz. His name means “dreamy” as his birth was foretold in his mother’s dream

Emese: Wife of Ügyek, mother of Álmos (meaning, sleepy). She was impregnated by a turul bird, which appeared to her in a dream and told her “a river will spring from your womb, which will flow and spread to a new land”. The táltos (shaman) explained the dream as saying that she would give birth to a son, who would be the ancestor of a great ruling family in a foreign land.

Bába: Meaning “midwife”, she was originally a good fairy who later degraded and became evil. Although she had magical abilities, she was not a boszorkány (witch). A Baba Yaga is a hard bargainer, and will threaten to eat those who do not fulfil their part of an agreemen

Bubus/Mumus: Feared Ogre or Bogeyman living in a cave.

Fene: A Fine, impressive or Heck of a demon, sort of undead curse. Today, a common saying still uses its name: “A fene egye meg!”, which literally means “Damn It!”, and is uttered when something does not occur as one wishes. “Fene” is also considered the place where demons roam, i.e. the popular Hungarian curse “menj a fenébe!” is equivalent to the English “damn!”. (Basically the devil.)

Garabonciás: One of the first Hungarian folk beliefs → supernatural force of personality. Also known as barboncás, verboncás, jowly student. The belief around to bringing the most important motifs, like the shaman → tooth or several teeth is born. Tattered robe, holding a book knocking on the houses: ask for milk or eggs; not much for him to be, but it should not be weighed out. Whole milk jug should be preceded, if eltagadják, tells us that there is milk in the house, and fenyegetődzik “will you give, but it will be too late.” As punishment storm, hail or cause the book “reads” the dragon and the ride over the village. The dragon’s long tail sweeps top of the houses, the trees and twist tövestől. (A Sorceror fond of Dairy).

Guta: A fearsome Hungarian demon who beats his victims to death, often associated with strokes, heart attacks, or sudden paralysis.
If Hungarians say about someone that he or she has been beaten by the Guta, it means that the person had a stroke of appolexy. (So says the pantheon.org)

Hadúr, or Hodúr in old Hungarian, short for Hadak Ura, meaning “warlord” or “lord of the armies” in Hungarian, was the god of fire, later became a war god in the religion of the early Hungarians (Magyars). In Hungarian mythology, he was the third son of Arany Atyácska (Golden Father) and Hajnal Anyácska (Dawn Mother), the main god and goddess. He had many brothers and sisters, including his two brothers: Napkirály (King Sun) and Szélkirály (King Wind). In Heaven, on the top of the World Tree on the first level there was the castle of Arany Atyácska, and Napkirály’s Golden Forest below it, and Szélkirály’s Silver Forest below it, and Hadúr’s Copper Forest was the third. There he lived as a blacksmith of the gods. He is thought to be a great man with long hair and with armour and weapons made of pure copper, since copper was his sacred metal. He supposedly made the legendary sword, Sword of God (Isten kardja) which was discovered by Attila the Hun and secured his rule. (Seems much of Dragon Quest came from Magyar myths, and middle earth).

Napkirály: Sun King, he is the Hungarian sun god and is the oldest son of Arany Atyácska (Dear Golden Father) and Hajnal Anyácska (Dear Dawn Mother), brother of Hadúr and Szélkirály. He rides his silver-haired horse from East to West every day, seeing everything below him.

Szélkirály: Wind King, he is the Hungarian god of wind and rain, and is the second son of Arany Atyácska (Golden Father) and Hajnal Anyácska (Dawn Mother), brother of Hadúr and Napkirály. His armor and weapons are made of pure silver, his sacred metal.

Szépasszony: Beautiful Woman/en, she is a female demon with long hair and a white dress. She appears and dances in storms and hail, and seduces young men. (Lady in White – South Park, sorry, had to add that).

Turul: The great bird resembling to a falcon that was sent forth by Isten to guide the creation and destiny of the Magyar people. The first kings after St Stephen I. were the hereditiary of Turul (“Turul nemzetség”)

Vadleány (Vadlány without plural): Wild Girls (forest), she is an elusive forest sprite who seduces shepherds, saps their strength and makes the forest rustle. She is usually nude and her long hair reaches the ground. She can sometimes be lured and caught with one boot (she tries, to put two of her feet to one boot).

Griff: It is a cruel, greedy bird eating humans, but it’s the only way to get back from Under World to Middle World.

Sárkány: A Hungarian demon. He has the power to turn people to stone. His function is to control the weather and he can be seen riding his horse in the thunder clouds. In some versions he is regarded as a dragon. He is depicted with seven or nine heads. Identified as Sarkany.

Some other spots…clearly the oldest joke in the world is “I don’t understand woman…”
Myths-Huns
Turul
Napkiraly
SZelkiraly
SZepasszony
Szepasszony: Monstropedia
Vadleany
Magyar Myths: Dicts
Sarkany