I've been wondering now ever since I've read some Norse mythology. It must be real since the runic magic is real, correct?
Norse Mythology is a particular cosmology, within which the Runes exist. Within Jewish Cosmology, you have the kabbalah; within Daoist Cosmology, you have Yin and Yang, the Five Elements, the Bagua, and so on.
Every spiritual cosmology is a way of organizing the spiritual mysteries of the universe so that they can be practically worked with. How real they are to you depends on how well the cosmology resonates with you. I've worked with the Norse runes as easily as I've worked with the Daoist five elements, so there are several cosmologies that are real to me. A more modern way to say it may be that they are all "real," yet subjective
ways of working with "real," objective
forces that are not objectively (scientifically) understood just yet.
It's hard for me to grasp it: is Åsgard like Heaven? Does it truly exist?
Asgard and Hel are not quite like the Christian idea of Heaven and Hell. If you learn mental or astral projection you can go there and see them for yourself, so they can be called "real" as far as any other astral realm is real.
The general pre-christian idea is "all souls reincarnate," so "heaven" or "hell" would just be the places where you go in between incarnations.
Can Àsatrù be anyhow compared to Christianity as a religion?
Asatru can be compared to Christianity as a religion, but Asatru isn't really what was practiced and believed by the ancestors. If anything, Asatru is a rather Christian way of practicing the Northern Way. If you read Edred Thorsson's books, he goes into explaining the old way a fair bit, and does so quite in a very scholarly way. In the mean time, you can look up "Teutonic" stuff, which is a word used to describe pre-Christian European religion. Northern Teutonic beliefs are the best preserved because of the Eddas, but these things were widely practiced across Europe.
Perhaps I'm just trying to comprehend too much at the same time. Perhaps I should just keep at the belief that there is only one true God (in Christianity) but what would that make the gods/goddesses of Norse mythology?
I'm mono polytheistic, where "from The One, comes The Many."
The Norse creation myth supports this, for me, so there's no internal conflict. Within the Void of Ginnungagap, Muspellsheimr and Niflheimr interacted to create all things. This is similar to the Daoist creation: within the Dao, Yin and Yang came forth. This interaction of Fire and Ice is a big part of Norse magic too -- if you look at the Rune symbols, they are all some combination of Isa (Ice) and Kennaz (Fire). I quite like to compare this to Yin and Yang, because the principle is essentially the same.
The deities of Norse Mythology, then, would just be residents of the nine worlds like any other spirit race (Vaettir). They are older and wiser than most humans and they govern the forces of the universe, and quite frankly I wouldn't want to make Thor or Loki angry, but none of them are beings that I idolize in the Christian or Hindu sense of "worship." I actually tried, since I came upon serious Northern practice right after exploring Yoga and worshiping Shiva. Suffice to say, worshiping Odin the same way I worshiped Shiva was not very...pleasant.
I actually think the Samurai treatment of the gods applies to this rather well: "Honor the gods, but do not rely on them." The same way most people are taught to honor their parents, but to get out and get a job as soon as they can.
Sorry, I shouldn't probably mix in the religion (I promise it won't happen again). It's just that I don't know how deeply I should get involved in Norse mythology. I don't know if I should be worried or not that Norse mythology enthralls me.
Don't stress out and over complicate it. If you're interested in a cosmology, study it and practice it. I do think it actually is important, in Rune Magic, to understand where they came from and the cosmology behind them. You could technically just use them, but it would be hard to master them out of their original context. Rune is an Old Norse word meaning "Mystery," they're not just letters. Initiation into the Northern Mysteries, in my opinion, begins with its cosmology. There is a reason story telling and story keeping was so big in this tradition.