Laws regarding taxes will be made more clear when a government can be formed and a national economy can established and is measurable. I would like to state I am not a tax professional, but i do pay taxes. As a Washington state resident working in the state of Oregon I pay taxes in two ways.
My federal taxes are dealt with my Oregon income taxes. This money is taxed because i get it through an employer licensed through the state. If my friend hired me for something or i sold something online, below a certain amount i do not have to report it thus making it tax free income.
The other way i pay taxes is through purchases made within Washington state. Although Washington income is still taxed through the federal government, the state instead taxes a flat rate varying between counties.
Now if i made income from a foreign body i would still be required to pay taxes but the rules become complicated and i could pay the required foreign taxes to supplement domestic taxes.
All that being said, i do not believe that the Asgardian government would tax an individual if said individual had no economic relation. When laws can be passed we will establish Asgardian licensed companies that deal in Asgardian goods and services. These will most likely be taxed to support the government and socioeconomic structure that the companies are based in. Since there is no current Asgardian territory, and people will be free to establish businesses anywhere, the complexity of international taxes will be a common issue.
My guess is that most citizens will only be required to pay taxes if they work for the government or an Asgardian business, and/or through purchases of Asgardian goods and/or services via sales tax. In the US the taxes you pay to Asgardia will most likely go dollar for dollar to what's required to pay from also being a US citizen.