In Wraith Night, Axe's modified Battle Rage enables him to be a very reliable tank. Because dealing damage = health gained, items like Blade Mail and Radiance sustain Axe's health more-so than items like Heart or defensive options like Assault Cuirass.

Skadi should be purchased after Radiance (if noone else buys it) as it trivializes the final boss--Wraith King's attack speed will be significantly reduced.