Asatru magick is a very broad category. We know that our ancestors used the runes for magickal purposes. We also know that certain people studied herbal lore, others practiced a kind of "low" magick. We have resources that indicate that something very like Native American Shamanism played a very important role in some of our cultures. There are mentions of sorcery and witchcraft in Sagas. There is probably no one, single, magickal "system" that you could point to and say, THIS is the Asatru Magickal system, though the runes and runic systems would probably come closest to that. However, my goal here is to simply indicate the many and varied paths that someone could pursue, all within the auspices of Asatru.
Runic - The runes are a very old magickal system. The runes are sometime referred to as the Norse or Viking Alphabet, sometimes they are believed to be a divinatory system, and sometimes they are referred to as a magickal system. Odin is said to have hung 9 days and nights on Yggsdrasil, and learned the secrets of the runes through that ordeal.
The Shaman is a person who has learned to see how all things physical and spiritual are all connected with one another. Through this web-like connection, wherein the action of one thing effects everything else, the shaman is able to perceive things to come, and to change the physical world. One of the main functions of a Shaman, historically, was that of healing. Shamans often utilize what might be considered "low" or "sympathetic" magick in order to change their environment, and help others. Shamans are very often loners who are very connected to the natural world, and who have a great affinity for animals, spiritual sight, intuitive leaps of understanding, and herbology.
Vitkis are magicians that practice "High" magick. Vitkis seek to master the runes and to develop means to alter their environment utilizing techniques of galdor, bind runes, and magickal rituals. Often, people who follow this path are termed Mages, Magicians, Wizards, Sorcerers, or something similar. The thing that separates "Vitkis" from any of these others is use of the Runes as their primary key to their magickal practices.
Witches were also known in ancient times, though often, as with Vitkis and shamans, they were often termed sorcerers (sorceresses), beguilers, poisoners, etc. I believe the most common term was sorceress, and at least among our ancestors, they were also known to use runes to help them accomplish their goals. Sorceresses and Witches are well versed in "low" magick and in Herbology. Sometimes these people worked harmful magick (as with poisoning, etc.), other times a village herbalist/healer might be described by those antagonistic to her as a "sorceress" in order to try to stir up popular imagination against her.
In addition to all of these categories and descriptions, there are prophetesses, visionaries, soothsayers, diviners, Healers of various sorts, and just about any magickal operation you can think of has some corollary within the Asatru tradition. Here at The Heathen Kinship we encourage study of Shamanism, Vitki, Seid, Mage-craft, divination, and Herbology.