Here`s info form official game site :
Quote:
Hrist prefers regales; Goodrid – shoes, belts, gloves; Hildr – weapons; Regin – shields and armor; Mist – artifacts.
To get the second level you should sacrifice one item to the Valkyrie. For the third and forth levels you will need 3 and 4 items accordingly. The maximum fifth level can be achieved only after finishing special quest, unique for each companion.
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So first Valk will accept only some item type not all of them, other junk item save for later when you get rest of you harem , cough,cough i mean Valk support team