Vinayaka Puarana and Mudgal Purana are Upa Puranas.
Some interesting information is found the Puranas about Ganesha.
Vinayaka Purana lists four Avatars of Ganesha.
Additional Five are found in the Mudgal Purana.
Some declare there are eight Avatars.
- Mahotkata Vinayaka (Mahotkaţa Vināyaka), who has ten arms and a red complexion. Different sources list his mount (vāhana) as either an elephant or lion. He was born to Kashyapa (Kaśyapa) and Aditi in the Krita yuga. The name Kāśyapaḥ (descendant of Kaśyapa) for Ganesha refers to this incarnation. This incarnation killed the demon brothers Narantaka (Narāntaka) and Devantaka (Devāntaka), as well as the demon Dhumraksha (Dhūṃrākşa).
- Mayuresvara (Mayūreśvara), who has six arms and a white complexion. His mount is a peacock. He was born to Shiva and Parvati in the Treta yuga. He incarnates for the purpose of killing the demon Sindhu. At the end of this incarnation he gives his peacock mount to his younger brother Skanda, with whom the peacock mount is generally associated.
- Gajanana (Gajānana), who has four arms and was born with a red complexion. He has a mouse as his mount. He is born to Shiva and Parvati in the Dvapara yuga. He incarnates for the purpose of killing the demon Sindura (Sindūra), who was so-named due to his reddish-pink complexion (see: Sindoor). It is during this incarnation that Ganesha gives the discourse known as the Ganesha Gita to King Varenya.
- Dhumraketu (Dhūmraketu) is grey in colour, like ash or smoke (dhūmra). He has either two or four arms. He has a blue horse as his mount. He will come to end the decline of the Kali yuga. During this incarnation he kills numerous demons. Grimes notes that there is a parallel between this incarnation of Ganesha and the tenth and final incarnation of Vishnu, where he will ride upon the white horse Kalki. The other difference is, Lord Vigneshwara tells Varenya that the whole universe and all the deva are created by him and ultimately everything will come back to him.
Another four are listed in the Mudgal Purana.
5.Vakratunda (Lord of the Twisted Trunk)
As Vakratunda, Ganesha embodies the formless spirit of the Universe or Brahman. In this avatar, He defeated the demon, Matsaryasura (Envy), who came into being when Indra, king of the Gods, once lapsed into absent-mindedness. Performing austere penances to Shiva won Matsaryasura the boon of fearlessness. He soon brought all the gods, including mighty Shiva, to their knees. Dattatreya, the unified form of the Holy Trinity, advised them to invoke Vaktratunda and divulged to them, the powerful seed mantra ‘Gam’. Their penance bore fruit – Vakratunda appeared seated on a lion and defeated Matsaryasura.
6.Ekadanta (Lord of the Single Tusk)
Madasura, demon of Intoxication, was the creation of Sage Chyavana. Shukracharya, guru to the Asuras, imparted to him the Shakti mantra of ‘Hrim’. Madasura meditated upon this mantra for centuries, until Shakti appeared and granted him the boon of fulfilling all his desires. Madasura ran amok and subjugated the three worlds. All virtue and goodness disappeared. The gods were then advised by Sanatkumara, Lord of Humanity, to invoke Ekadanta.
Seeing Ekadanta’s blue-skinned, terrifying form, seated upon a mouse, Madasura surrendered to the Lord. Ekadanta spared him but commanded that he never appear in places where the Lord is worshipped with true devotion. Madasura however, was left free to enjoy the fruits of any activity imbued with demonic qualities.
Avatar in Sanskrit means “descent”; in Hindu mythology, a deity descends from heaven to earth for a specific purpose. Sacred texts like the Ganesha Purana and Mudgala Purana state that Ganesha assumed eight avatars, each manifesting in a different epoch and descriptive of a single attribute. All the avatars had one purpose – to slay a demon.
However, Lobhasur accepted his defeat without any fight.
During Samudramanthan, When Lord Vishnu had taken the form of Mohini, Lord Shiva had got attracted towards her. He had ejaculated that time and a monster called Krodhasur was born. Krodhasur had pleased Lord Sun and received in blessing to rule the world.
This avatar of Lord Ganesha had defeated Kamasur monster.
This avatar of Lord Ganesha defeated Mam (born from Parvati).
This had created fear in every God’s mind. When he went out to fight, Lord Ganesha took the avatar of Lambodar and stopped him. Krodhasur then went to Pataal lok.