Prehistory and origin of Stockholm
According to the Chronicle of Eric, written in the 1320s, Stockholm was founded by Birger Jarl around 1250 as a lock to the Lake Mälaren region ("laas fore then sio", "lock before that lake") in order to prevent pirates from reaching the seven cities and nineteen parishes around it. Another medieval source ("Visbyannalerna"), however, claims the city was founded in 1187 following a pagan pillaged the city of Sigtuna, and as there was an "Earl" named Birger around at that time too, the disputed origin of the city are likely to remain obscure and some historians choose a diplomatic interpretation saying there was some sort of fortification around by the mouth of lake Mälaren when the city was founded during the second half of the 13th century. As Snorri mentions no city in his account but some sort of fortification called a "kastali" (in various manuscripts curiously said to be located east and west of "Stocksund"), it has generally been assumed this fortification eventually developed into the castle Tre Kronor located where still is the Stockholm Palace.
Stockholm during the Swedish Empire
On "Malmarna", the surrounding ridges, the first suburb to catch the focus of Oxenstierna was the western part of Norrmalm. A city plan for the district, most likely developed by Anders Torstensson in early 1637, feature several still preserved structures, including "Stoore Konnungz gatun" ("Large King's Street", today's Drottninggatan) and "Mönstre Platz" ("??", today's Hötorget). 
A second devastating fire in 1640 on the eastern part of Norrmalm provided the excuse for a city plan for that district, and at the same time the rural area east of Norrmalm ("Ladugårdslandet", today's Östermalm) was donated to the city. Soon Torstensson presented a unified plan for all three northern suburbs, long after his death realized with only minor changes. One of the problems he failed to deal with was the huge ridge Brunkebergsåsen separating the two parts of Norrmalm, and misfits between the non-aligned streets on either side can be seen on modern maps of the city.