Story of Modak
Ganeshji is very fond of 'Modak'. Mod means happiness, who likes joy is liked by Ganeshji. Modak comprises coconut, jaggery, cardamon powder, poppy seeds, and rice flour. Ganeshji likes Panchkhadya modak which consists of dry dates, raisins, cashewnuts, powdered sugar and candy. These 5 Panchkhadya symbolised 5 types of pleasures.
1) Subjective pleasures
2) Worldly pleasures
3) Meaningful pleasure
4) Joy of enamampication
Story of Durva
There was a demon by the name of Analasur who made the lives of the people miserable on the earth. All the Gods invoked Lord Ganesh so Lord Ganesh took on Analasur. Analasur ran after Lord Ganesha to kill him. But Lord Ganesh devoured him but it caused terrific burning sensation to him and burning could not be mitigated by any means. All the Gods tried there level best to palliate this burning sensation but all the efforts went in vain. Then one sage came and he bundled 21 'Durvas' (cynaton' into one bundle in this manner he made 21 bundles, invested with mantras and those bundles were offered to Lord Ganesh, which relived him of burning sensation.
The Ganesh Puja Durva having 3 or 5 stocks is generally used. The three stocked Durva is offered with a view to nullifying the bad effect of destiny, collective fate and Karma. 5 stocked Durva is offered with an eye to getting the atmost signifinance of all the 5 prequisites and individual is gifted with.
Story of Shami Patra
Shami Patra is also called as "Vanhipatra". Shami is very dear to Lord Ganesh. So Shami is offered to Lord Ganesh.
Once Parvati asked Lord Shiva why Shami is so dear to Ganesh, then Lord Shiva narrated the story. Once upon a time there was a King "Priyavrat". He was very religious and great. He had two wives, Kirti and Prabha. Prabha had a son whose name was Padmanan. The boy was brilliant. So when he was just 5 years old his thread ceremony was solemonised. Prabha once insulted Kirti. So Kirti, decided to commit suicide . But one priest by the name of Deval intervained and suggested her to worship Lord Ganesh. So Kirti offered great penance to Lord Ganesh and in place of Durva she offered him Shamipatra invested with mantra. It pleased Lord Ganesh no end and she also gave birth to a son named Shiraprasadan. When Shirapraprasadan was 4 years old someone poisoned him and child was dead. That very moment Lord Ganesh's great devotee arrived there sage 'Gutsamand'. He advised Kirti that the 'Punya' she had collected by offering Shamipatra she must dispense with that so that her son could be brought back to life. Kirti did what the sage had advised, and he was brought back to live. And Prabha got afflicted with great incurable element. Then King started treating Kirti nicely.
Story of God of Gods
There was a demon called Gajasura. He was all-powerful and an ardent devotee of Lord Shiva. He underwent penance for many years to receive special boons from Lord Shiva. Lord Shiva, the god, who is easily pleased by prayers, is deeply moved by Gajasura's devotion. He blesses the demon and offers him a boon. But the devotee is not as innocent as Lord Shiva. He pleads with Lord Shiva to reside in his belly. Left with no option but to grant the boon, Lord Shiva gets into Gajasura's stomach.
Meanwhile on Mount Kailash, Parvati - Lord Shiva's wife becomes anxious not knowing the whereabouts of her husband for a long time. She searches through the whole universe but to no avail. Finally she approaches Lord Vishnu - the preserver of the world. Lord Vishnu assures Parvati to find Lord Shiva out. He disguises himself in the form of a street player along with Nandi - the sacred bull of Lord Shiva and sets out in search of Lord Shankar (another name for Lord Shiva). They go to Gajasura's kingdom and Nandi performs a dance to please the demon. The demon is delighted to see the bull dancing in his honor and wishes to reward the bull. The bull asks for Lord Shiva as a reward. Hearing this, the demon realises that the entertainer is none but Lord Vishnu himself. He also realises that Lord Shiva cannot be made to live in his stomach forever because he has his role to play in the world. He lets Lord Shiva out of his stomach. But he prays to him, that he be made immortal in the memories of people. To fulfill this wish, Lord Shiva severs Gajasura's head and frees him from the cycle of birth and death. He carries the head along with him. On Mount Kailash, in the Himalayas, Parvati comes to know of Lord Vishnu's victory and is very happy. She makes arrangements to receive her Lord and goes to bedeck herself. She wants somebody to stand guard. So she creates a doll out of the dough that she uses in her bath. She calls him Vinayak - the one who puts off all obstacles. This boy having never seen Lord Shiva, prevents his entry into the palace. In a fit of fury Lord Shiva beheads the boy and enters the palace. Parvati is unaware of the happenings and receivesLord Shiva with warmth, for he had returned after a long period. During the course of their conversation, Lord Shiva mentions the incident at the palace gates and tells her about severing the child's head. Parvati is shocked to hear the news and pleads with Lord Shiva to bring the child back to life for he is like a son to her.
Lord Shiva who has with him the head of Gajasura, immediately puts it on the torso of the dead child. Thus the child comes back to life. That day is Bhadrapad Chaturthi. Lord Shiva blesses him with a boon that the entire world would worship him on that day and also would propitiate him before any auspicious event.
At the same time, all the Gods approached Lord Shiva and requested for a leader. To select the best one of Ganseh and Kartikswami as a leader of all the Gods, Lord Shiva conducts a test between the two. He says that whoever makes three rounds of the earth sooner than the other, will be made the Ganaadhipati. Kartikswami seated on a peacock, his vahanam (vehicle), and starts off for the test. Vinayak is given a rat which moves swiftly. Vinayak realises that the test is not so easy but he cannot disobey his father. He reverently pays obeisance to his parents and goes around them three times and completes the test before Kartikswami. He says, " my parents pervade the whole universe and going around them, is more than going round the earth." Everybody is pleasantly surprised to hear Vinayak's logic and intelligence. Meanwhile, Kartik is amazed to see Ganesh completing the holy bath at each river that he reached at and ready for another round of the universe. When he comes back to Kailas, Lord Shiva had already declared Vinayak as the winner. He is blessed as the Supreme God of the universe. After this, Vinayak is called as Ganaadhish, Ganpati and Ganesh. All the gods worship him.