I am a U.S. citizen based in the U.S., working remotely as an independent contractor for Norwegian companies with work in Norway (interpreting and voice over). I have to pay taxes on my income in the US, but does the Norwegian company have to file a 1099 or can it just be treated as "other source" income? Similarly, do I have to pay Norwegian income tax?
Whether the Norwegian company has to file a 1099 is a matter for that company. From your perspective, you report the income on your US income tax return, and if they send you a 1099, you include it. If they don't, it's not a problem that you haven't included one with your return.
I am fairly certain that you do not need to pay Norwegian income tax, since you are working entirely outside of Norway and do not reside in Norway, but I am far from certain. However, it looks like you may need to collect value-added tax and remit it to the Norwegian revenue authority. I'm not sure whether this would count as "electronic services," but if it does:
VAT On E-Commerce - VOEC
Foreign providers of electronic services to Norwegian consumers are obliged to collect and pay VAT. From 1 April 2020 this also applies to suppliers of low value goods.