Let's take Ghenghis first:
His focus was on northern China, and central Eurasia. His primary focus was central Eurasia. He led the conquest through what is now Khazakhstan and Uzbekistan and then down into the Kush of Afghanistan. He left much of the work in northern China to subsidiary forces. His last military action was the destruction of the Xi Xia in northwest China. We cannot know if he planned to take the Song, but it is clear that he wanted northern China. So there is the issue of focus, you cannot take over every region all at once. EDIT - PART 1.

PART II - One of the best reasons why we know Ghenghis was interested in Northern (if not all) of China was his meeting with the Daoist monk, Qiu Chuji. Qiu was initially summoned by the Khan up to Beijing, then when he found the Khan absent, he went on to Mongolia. There he discovered that the Khan was deep in the Kush. With some prodding from the Khan (via letter), Qiu decided, though he was ci. 80 years old, to make the trip. Thankfully, we have a diary style account of the journey and subsequent meetings with the Khan. It seems Ghenghis wanted Qiu to give him secrets of achieving immortality, for which Qiu was known. Qiu told the Khan that he could not help with the quest for immortality, and instead gave the Khan some advice on how to better rule the people of China.
The Khan was pleased with the meeting and sent Qiu back with a very significant title - Overseer of religion in Mongol occupied China (at this point about half the Jin territory). Qiu used his power to bring millions into adherence with his Daoist sect, largely because they were given full protection from mongol forces in the north, and to curb Buddhist power. He and his successors closed down many Buddhist monasteries and temples, which led to a backlash after Ghenghis died, and more Buddhist-friendly administrators took over the north.
The point of all this is that we must see Ghenghis' attempts to establish strong ties with one of the largest sects in the north as part of a greater plan to win Northern China.

Now, to Ogedei -
He did not wait long to continue his father's work in northern china. Within 10 years of Ghenghis' death, by 1237, Ogedei had fully subdued the Jin territories, and made some inroads into the Song territories. It is not clear whether he wanted to take the Song, but he had to keep fighting, because Song officials kept assassinating his envoys.
So, he tried, but failed to break through, for the same reason it took so long, and such massive effort for his nephew 40 years later, the Yangze was a formidable defensive position for the Song. The Khans would see no natural barrier so significant in all their conquests. The Song were also rich and powerful (though often ambivalent to the point of paralysis), so taking their territory was no cakewalk. Nonetheless, Ogedei began a process that would ultimately take almost 60 years to complete, resulting in the total conquest of song China.

I assume these are different questions namely:

-Why didn't Genghis Khan attempt to invade the Song Dynasty?

-Why did Ogedai Khan fail at invading the Song Dynasty?

Yeah?