Rapidly changing environmental and geopolitical equations on the eve of Rajsooya yagna.
Partition of Kuru clan - The barren region which formed rapidly dessicating Yamuna-Saraswati basin was given to Pandavas, while Ganga basin was kept for Duryodhana. This is where Vrishnis enter the politics of North India, IMO. Krishna establishes very cordial relations with Pandavas, who just like him were thrown out of their secure power-base and were forced to establish a new power-centre in apparently resourceless land which offered dwindling prospects in long term. Furthermore, bulk of this land was forest land inhabited by Naga people.While decreasing rains were making bushfire increasingly frequent in the region, the monsoon rains used to arrive timely and prevent the fires from spreading. For bushfire to occur, the grassland must be sufficiently dessicated and high temperatures and wind-velocity. All this is seen Punjab (the salt-range of Khushab) and also in northern Rajasthan. However, just when conditions reached optimum, rains arrived, thereby making the bushfire impossible.
The Forest burns and so do people
Vrishni-Pandava alliance decided to take advantage of this phenomenon and clear off the forest of Khandava in order to create arable land and space for living and building cities. They "somehow" managed to divert the rains from that region and started a gigantic forest fire while encircling the forest region and killing off every Naga and Asura people dwelling in that forest. After a week of battle, the region was "cleansed" of Naga people and forest and was made fit for "civilization" and "urbanization". Few survivors managed to escape this carnage, under leadership of their king "Takshaka" who escaped to Upper Sindhu valley and founded the city of Takshshila (modern Islamabad). The Naga and Asura architects who surrendered helped Pandavas in their project of "Indraprastha (modern Delhi) construction". This shows higher skills of Nagas and Asuras in civil engineering. These contacts were also used by Vrishnis to develop their own city of Dwarika (the defenses of which were designed by Mayasura who was captured as PoW from Khandavaprastha).
The great game of competing political interests for supremacy of Sapta-Sindhu region
The axis of power from Dwarika to Indraprastha was forming as an "Anti-Kuru" lobby and alternative to Magadh Lobby. The "confused" Panchalas had by then decisively shifted in camp of Dwarika-Indraprastha axis permanently owing to marital relations between Pandavas and Draupadi. While Pandavas did not have any animosity towards Magadh, it was crucial for Vrishnis to settle the "problem of Magadh" once and for all. Magadh's sphere of influence had already reached Avanti (Ujjain) where the Yadava kings (Vinda and Anuvinda) were staunch allies of Jarasandha. Jarasandha was stealthily encircling Kurus, while they were busy infighting and partitioning their land. This ring of encirclement had potential of breaking off Dwarika from rest of India. Hence the urgency to finish off Magadha's influence was pressing as far as priorities of Vrishnis are concerned. Krishna had managed to establish marital relations with several yadava kings which were under Jarasandha's influence. He started with Rukmini (the princes of Vidarbha). He also married princess of Ujjain and few others. He also took wives from Vrishni clan as well to cement his position in clan and garner support from his clan members. Yet, the noose of Magadh was tightening around Kuru, Indraprastha and Dwarika.
While Pandavas were still part of Kuru dynasty, Duryodhana had given kingdom of Anga (northern Bengal) to Karna. While Pandavas were in their first exile (after Varnavat-Laakshagriha episode), there was one very important event which is usually downplayed. In Kalinga (Orissa), Karna defeated Jarasandha in duel. This had increased the prestige and influence as well as power-projection ability of Kurus in eastern India. Karna's devotion to Kurus is legendary. Karna's influence in Bengal and over Magadh directly corresponded to Kuru influence in Eastern India.
Thus, while Kurus were rather strong and playing their own moves to encircle Magadh, there was no such strategy in think-tank of Dwarika-Indraprastha axis (DI axis) which could tackle with these two great games. It is from here, that character of Krishna starts raising above rest of people, just like Michael Corleone in Godfather-1 (sorry for this metaphor, but Michael Corleone is the closest comparison of the master game that Krishna played). The scale and intricacy of Krishna's game is million times more than the one played by Michael in Godfather Saga. But it comes very close in principle. I would urge gentle readers to remember the strategy of Michael Corleone to kill off the heads of 5 mafia families in NY in one fell swoop and then subsequent moves to consolidate the space in the power-vacuum.
The Turning point
Krishna used his personal influence over Pandavas to make them understand that the interests of Dwarika and Indraprastha coincide. That, it was equally important for them to tackle the tightening noose of Magadh and that they had no option but to strike at place where Magadh expected least. Magadh was traditionally a autocratic polity. Absolute power was consolidated in the hands of Jarasandha, and his son was not as strong-willed as his father. Elimination of Jarasandha from political scene of India was "the key" for all the problems which DI-axis was facing OR was going to face, in absence of any leverage in "backyard" of Magadh like Kurus had in form of Karna.
The action of Krishna-Arjuna-Bheema trio is similar to escapade of Shivaji while his raid of "Lal Mahal" in Pune in the bedroom of Shaistekhan in dark night when he was least expecting. The act was more psychological operation than a military one. The gamble of challenging Jarasandha in duel paid off. Whilst Jarasandha was an extremely accomplished warrior, Bheema was younger and more agile. Furthermore, Karna had defeated him in duel few years ago. While Karna pardoned Jarasandha, Krishna had no intention of doing so. He proposed duel-until-death, which was accepted by Jarasandha and by stroke of luck in favour of DI-Axis, the result of this duel came in favour of DI-axis and in one stroke, the entire strategy of Magadha fell to shambles. Immediately after this victory, Krishna raided regions as distant as Kaamroopa (Assam) and defeated Narakasura, established his son Bhagadatta on throne. Defeated king of Pundra (central Bengal) Paundrak Vaasudeva and killed him in battle. Jarasandha's son Sahadeva was established on throne of Magadh and his sister was married off to one of the Pandavas (I think Nakula).
Aftermaths - Spoils of victory
While Harivamsha says that Eastern conquest of Krishna was while Jarasandha was alive, I think this does not make sense given the entire political setup which I have described above. As far as my understanding of Krishna as a politician goes, he would't have ventured there while Jarasandha was still alive. It was simply too risky. But, these are my views, hence take them for what they are worth.
Coming back, Krishna coaxed Pandavas to go for similar "Dikvijaya" and perform Raajsooya Yagna. There is something about Raajsooya Yagna that even Sri-Raam dared not to do it. Raam preferred Ashwamedha instead. What made Yudhishthira so confident to perform this Yagna is mystery. Four Pandavas ventured in four directions and came back victorious and wealthy. The Indraprastha, Dwarika and the DI axis was recognized by India as the legitimate power-centres and defacto leaders of "anti-Kuru" lobby. DI-axis won many friends (those kings imprisoned by Jarasandha were released by Krishna and they instantly became allies of DI-axis. The Eastern India was secured by raids of Krishna and Bhima. Except solitary "Anga", rest of the east of consolidated and befriended by and large.
In Raajsooya sacrifice, the last remaining commander of Jarasandha, Shishupaal, was finished off by Krishna, thus completing the victory of DI-Axis. Now, DI-Axis had completely encircled the Kuru dynasty. Had consolidated vast stretch of India, which Kurus and Magadh were vying for. Won friends in most unlikely of places. The victory of DI-Axis was complete. All stories should end here. Since the story did not end here, that separates Mahabharat from rest of tales.There are plenty of things to learn from this "Itihaasa" of India. Those with sufficient political acumen will understand the modern relevance of this story.