I have been offered a job transfer to Oslo, Norway from my current employer in UK. I do not know the living costs, taxation and the salary that can be expected for an IT Solutions Architect role.
What would be the comparable salary in Norway if the person is earning £70,000 / £80,000/ £90,000 in London UK
Norway has quite a high cost of living, but salaries there tend to keep up with the cost of goods, services, accommodation, etc. Taxation in Norway is, unfortunately, quite heavy, which is part of the reason it costs so much to live there.
Will you be living alone or with children? I'm not entirely sure on what a comparable salary to the one you're earning now would be, but what I'd suggest is using cost of living websites such as Expatistan and Numbeo to draw up a rough list of expenses. Then plug in the figures from the website to see how much, roughly, you'd need to be earning to maintain your current lifestyle.
You can also have a look at our Cost of Living in Norway page for an overview.