hm, don't know what you mean with fighting stuff! i'm not going out with my axe and burn churches and slay christians , if you mean that! but the viking era was the beginning of the end of the native germanic religion(well not REALLY the end as you can see), yet their faith was the norse religion. they fled their homes in norway, sweden and denmark because missionars from the south were allready trying to force christianity on them and kings in scandinavia were tryingto unite the villages and towns to kingdoms! of course the first thing onr assiociates today with Asatrú are vikings and of course the are an element in the history of this religion, but not all! remeber that the west-germanic tribes(todays english, dutch and german), were already christianized at this time, but once they had the same faith as their northern brothers. we are calling the allfather Wotan, while in scandinavia he's named Odin. even today you see this influence in "wednesday", Wodens(anglo saxon for Wotan) Day!
if you're refering to stav, the germanic martial art, i have to say that i don't have any skills of it, but would like to learn it.
i do follow Ásatrú as much as i respect nature, and have a special spiritual connection to it(specially of my country and to countries of similar cultural background) aswell as the old custums and myths. i celebrate the pagan hollydays. i read the germanic sagas a lot. i lead a healthy life and i despise most of todays plastic "culture" like mcdonalds or other "cultural enritchment" from the usa(sorry, no offence to the american guys, but you have to understand that the "american way" is not suitable for all the world). i do blóts, hopefully more regular in the future and celebrate summer/winter solstice.
since you live in iceland and Ásatrú is an officially recognized religion there you shoul have quite some knowledge about it!