In Canada (and many others), foreign countries can be represented in 3 different ways: #1 a diplomatic mission (embassy), #2 a consular post (consulate), #3 International Organizations and Other Special Representative Offices (office). Since Asgardia is not recognized as an autonomous country yet, the third option seems more viable. However, to create an embassy/consulate/office, we need to be at least recognized by the host country (not necessarily the whole UN), as it agreeing to cede a part of its own territory. To get such political territories, we need to be officially recognized first (at the UN, or under the host country's own recognition criteria).
However, there's nothing preventing us to create Asgardia themed parks, stores and hotels... but, since we're a small nation, we need the official agreements to use the trademarks/intellectual properties (since probably not in the public domain yet) and probably some sort of "reports of good standings and motivation" under some guidelines and restrictions (to not tarnish Asgardia's name, or to not misuse/corrupt its very essence). I don't know if our government is bureaucratically organized enough to manage such lucrative ambitions yet. Since having no territories on Earth, such "embassies/themed parks/stores/hotels" could be enough to get an economy of our own, with our own currencies... ones of the few requirements to be acknowledge as a nation by the UN.
p.s. Celestia, a space nation create in the late 40's (now "extinct") had it's own currency, and its flag once flew at the UN. In one year, Asgardia already count 100X more citizens!