Theoretically, the Berserker is designed for one thing only: going on the offensive. Norway's civilization ability allows it to quickly traverse the seas and reach enemy lands on other continents. With 4 Movement and a Combat Strength of 50 when launching attacks there, it can make quick work of most of the units and cities of the Medieval Era while laying waste to every district and tile improvement in its path. A few Berserkers backed up by Crossbowmen and Harald Hardrada's Viking Longships will spell doom for most coastal civs.
In practice, it is actually pretty hard to wage a full-on war with this unit, as it is too squishy on defense compared to other units in the same era. Think of it as a 1 Range ranged unit, strong on offense, weak on defense, which already makes it pretty bad, as ranged units with 1 Range cannot focus fire very well, and expose themselves while doing so. The Berserker is even worse than that, since it also takes damage on offense. Since this unit has to be hard built, you can easily waste a lot of Production on a unit that can die so quickly. Therefore, it is actually better to use this unit as a "land" Viking Longship and focus on pillaging and claiming tactical tiles only. Once in a while it can capture a city or finish off an enemy unit near death, but try not smash this unit into a full health one like how you use other melee units.
Civilopedia entry Edit
According to a number of Old Norse sources, the berserkers (Ulfhednir or “Odin’s special warriors”) were Vikings who fought in “an uncontrollable, trance-like fury.” Other sagas note they forsook armor and went into battle bare-chested wearing wolf pelts, and were “mad as hounds, bit their shields … they slew men but neither fire nor iron had effect upon them.” Pretty impressive, even to the other fun-loving Norsemen. King Harald Fairhair supposedly used them as shock troops in the front ranks of his army c. 800 AD, and other Norse kings kept some as royal bodyguards, depending on their fierce reputation to keep the unruly in line. As the pious Christians said, “From the fury of the Norsemen, good Lord, deliver us.”