Upvote:5
When applying for [ESTA], which address do I add?
It doesn't much matter. I'd probably suggest the address in Norway, especially if you're there for longer than a few months.
My passport address is therefore not the same as my actual one.
That doesn't much matter either. Many countries' passports don't disclose the address at all. If you're asked about the discrepancy, just explain that you're a student and you therefore have two addresses.
I'm also flying from Norway to the US.
That also doesn't matter, since of course you could be a Japanese citizen residing in Cape Town but flying to the US from Norway.
The important data points are those establishing your identity and that of your passport, and the important questions are the ones concerning your eligibility to travel to the US (the odd ones about your terrorist activities and that sort of thing).