Talk to a qualified accountant who is familiar with this situation!
There is a US/Norwegian tax treaty - the full text in English is here.
You didn't actually say but from context it appears that you are a Norwegian tax resident - under the treaty you will remain so, maybe (Article 3(2)). If you are a tax resident of another country then you will need to read any treaty between that country and USA and/or Norway.
If you are a salary or wage earner (which it sounds like), then Article 14 applies. Provided you are in the US for less than 183 days in the tax year then you will be taxed in Norway and not have to deal with the US IRS. However, this is just over 6 months and you have indicated you will be in the US for 7, so it depends on how much of this is within a single tax year.
If you cross over you will need to lodge returns in both countries and will be taxed according to the laws of both countries (including the treaty) - this will be messy.
Assuming you work for the same Norwegian employer for the full year, they will deduct taxes and pay them to the Norwegian government. 5/12 of this will be domestic (Norway) and 7/12 will be foreign (USA) income. When you lodge your return in Norway you will get a refund, when you lodge in the USA you will have to make a payment. It is unlikely that these amounts will be equal - you may end up paying more or less tax - you need to know this so you can negotiate compensation with your employer if you are going to lose.
Remember it is you who are responsible for paying your tax, not your employer.
