Author's Note: Just a basic outline since I'm quite busy at work.
980s: A Viking expedition, led by the Rus lands in Azerbaijian. The Rus have many Pecheneg, Oghuz and Bulgar mercenaries with them. They march overland, sack Tabriz and call it a day.
The huge haul of loot from Tabriz begins to attract the eye of many poor people in the Rus Kingdom as well as Turkic tribesmen on the steppes searching for loot.
The next expedition is larger and results in the local Rawadids being forced under the Varangian boot. The invading Norsemen are still pagans at the moment and Vladimir is waffling between religions still.
1000s: Further Varangian probes down the Tigris and Euphrates force them into conflict with the Daylimites and Hamdandids. However, repeated Varangian military successes against Iranian and Arab forces increasingly weakens both dynasties. The Varangians traveling down south are becoming increasingly Turkicized and Persianized by their contact with Middle Easterners. Eventually, the Buyids fold under Norse pressure and become a tributary of Tabriz. Baghdad is spared a sacking only when the Buyids pay a massive bribe to the Varangian chieftain.
1050s: The Tabriz Varangians annihilate the Seljuk Turks at the Battle of Baghdad in 1055. Varangian naval skills insure that the Seljuks fail to cross the Tigris.
Oleg, the Varangian chieftain of Tabriz, is given the title of Sultan by the Abbasid Caliph. In search of more loot, he loads up his ships again and subjugates the Kingdom of Oman. Due to a lack of interest, Oleg also signs peace treaties with Georgia and the Eastern Roman Empire.
Late 1000s: The Seljuks are diverted into India. The Gangetic Plain is thoroughly looted and subjugated by hordes of Turks. The Varangian Sultanate becomes extremely wealthy as Norse and Omani sailors ply the waters from East Africa to China.
Yaroslav, one of Oleg's grandsons, decides on a larger prize. Loading up his ships once again, he lands in India, near the port of Cochin. He seizes the port and declares independence from Baghdad. The Sultanate of Cochin is the first Norse polity in India but it won't be the last.