Historically, Sweden has made multiple attempts at building a large empire, some of which were successful. The country still has a king (the current being Carl XVI Gustaf).
Kingdom of Sweden
Immediately, in 1066 you have a simmering crisis on your hands, in the form of your heretic Jarl of Uppland brother. He has almost half your kingdom and can raise a large number of troops. By using honorary titles you can hasten or delay the showdown rebellion. I prefer to put off the day of reckoning, and try and gain a greater advantage for when this war takes place. You definitely want to institute Limited Crown Authority before this war, so if you do win the war you can revoke a title out of it.
You can press your ducal claim to Dal, gain a little prestige. Throw a feast and build up your relations with your other vassals. Hopefully you can have more than your heretic Jarl brother and crush his forces.
When fighting against Duke Erik III "The Heathen" of Uppland, use the river crossings near Sodermanland, Narke, and Varmland to give your troops an advantage. Also, he spawns childless, so he wills his land to king Svend of Danmark until he has a child. However, his wife is much younger than him and usually has at least one child before or during a war with him. He is also not as skilled fighter, diplomat, or ruler, so do not worry about him.
Picture: Duke Erik III the Heathen, your brother-in-law and traitor. He is also the uncle of your sons should you succumb to pneumonia before a war with him. Defeat him in war and revoke his titles.
You have a ducal claim to press on Norway, but Norway begins as one of the strongest Kingdoms. Build yourself up first, and increase your income and levies. You'll need to build a significant demesne, you may want to acquire the counties of Narke, Dal, Östgötland to build your demesne. You'll want to build your holdings around the many holding counties in Östgötland, Småland rather then in the north or Finland where the counties are usually 1 or 2 holdings.
Invading the Pagans
A huge source of titles can be found in the Duchy of Norrland, Kingdoms of Finland and Livonia. Move quickly to seize titles as quickly as possible. Norway, Denmark and the Slavs will be trying quickly to attack the pagans, so move more quickly than them. You could acquire the Kingdom of Lithuania or Finland if you are aggressive enough. You will need a number of titles to give to your many sons. Your Court Chaplain should continuously be trying to convert the populace and bring religious uniformity to your realm.
Heirs and Succession
Picture: Your eldest son Erik. Like all of your sons, he is young and unmarried, so marry him off before even thinking of giving him land. He is also a decent commander in wars against Erik III or the pagans
You start off with only 5 members of your dynasty, yourself and your 4 sons. King Stenkil also spawns with the pneumonia trait, so there is a chance he will die with a few days of reigning. Be sure to immediately pick your son before unpausing. Erik (eldest) tends to be best but any of them will do, none of them have any distinct advantage over the other.By default, the youngest son Name is hier, but it is easy to influence the cote in your favored heir's favor. Beware of the Duke of Smaland, as he usually votes for himself and can convince other voters to nominate him. It would be a shame if he was heir and a tragic accident were to happen to him....Historically, Erik Stenkling inherited the crown but was forced to fight his uncle, his father's brother-in-law, in the War of Two Eriks, where Erik of Uppland was killed on the battlefield and Erik Stenkling died of sickness from the cold Swedish winter. His brothers Inge and Halsten succeeded him.