The notion of a blue berserk mixes together two mostly-unrelated cases: that of Berserkers, or berserks, “Norse warriors who are primarily reported in the Old Norse literature to have fought in a nearly uncontrollable, trance-like fury” [1] and Celtic warriors, which “Julius Caesar in his Commentaries on the Gallic Wars” described as dyeing their skins blue [2].
Note that while woad [3] (or, Isatis tinctoria [4]) produces a nice blue dye, it is not at all clear that woad actually was used by Celtic warriors for skin dyeing. Source [2] says: “experimentation suggests that woad is not very well suited as a skin dye nor as tattoo ink”, and source [4] suggests that the vitrum coloring agent mentioned by Julius Caesar may instead have been “some form of copper- or iron-based pigment”.
[1] Wikipedia, Berserker
[2] Wikipedia, Celtic warfare
[3] Wiktionary, woad
[4] Wikipedia, Isatis tinctoria