I'm flying to Tallinn, Estonia via Oslo with Norwegian. I need to enter Estonia on my Estonian visa, and thus cannot be stamped into Schengen beforehand as this will cause complications. If I'm transiting through Oslo for 1hr 30mins, will my passport be stamped?
I need to enter Estonia on my Estonian visa,
You will be entering Estonia on your Estonian visa.
and thus cannot be stamped into Schengen beforehand as this will cause complications.
Why not? What complications will it cause?
The stamp that you get from Norway will look just like the stamp you'd get from Estonia, except that it will show that you entered the Schengen area in Oslo instead of through an Estonian border station, and it will bear an "N" for Norway instead of an "EST" for Estonia.
As Thomas Cruise suggests in his answer, requiring people to enter the Schengen area through the country that issued the visa makes no sense, and in fact there are several points where the Schengen regulations specifically contemplate people entering the area through a country other than the one issuing the visa or even require it.
This is why I asked for clarification of the complications you anticipate. If you have some source suggesting that you need a passport stamp from Estonia, perhaps we can help identify whether you have misinterpreted the source or whether it's simply incorrect.
If I'm transiting through Oslo for 1hr 30mins, will my passport be stamped?
Yes it will. There is no way to avoid this other than to change your ticket so as to fly to Estonia from an airport outside the Schengen area.
Schengen area is a single border control area. You pass through passport control at the first port of landing in the Schengen area and last port of departure. You don't need to land in Estonia on an Estonia visa and it doesn't cause any complications.
Schengen has been in existance for decades and countless people travel in and out everyday. Not all 26 Schengen countries have wide connectivity. A significant percent of people use larger airlines like KLM, Air France, Lufthansa etc to enter the Schengen area and thus pass through immigration in the Netherlands, France, Germany, etc. regardless of where visas or residence permits were issued from.
It is a non-issue.