Berserkers look like threat, but actually, they are very vulnerable to...everything. They are big, with nonexistent evasion skills. They are slow and has mediocre aim for a melee stomper. They are organic and has no armor unlike its "lesser" version: the Mutons.
Berserkers are large Mutons with sole melee attacks. They don't dodge, they don't take cover, they run into everything or anything even if there are acid, fire, or poison pools, they will cross them to punch your soldiers' faces. Berserkers have large pool of health points, but you can easily take them down because of the reasons stated above. Everytime you land a hit on them, they get "Enraged" and when they do, they attack units near them, even if they are their allies. So, hit them hard and from afar. It is not really recommended to go near them as they can easily wipe a human soldier out of the planet in one Hulk Smash.
Berserkers are great candidate for mind-controlling madness as they have large health pools. You can mind-control one and then send it all over the map to trigger encounters. They can survive heavy fire because most of the alien attacks are not effective towards a Berserker. Or they are just that beefy!