Nunu's farming is pretty bad. His attack speed is very slow which makes it hard to get cs. He doesn't have any wave clearing moves but his W is able to kill a few low health minions while you are channeling it to get the enemy champion.

Pros
He is able to stun very well with his W
He is good against champions without a rooting and stunning ability: Kayle, Dr. Mundo, Jax, etc.
Life steal mid and late game is very good
His ult is very good even when you first get it
Ult cool down is very fast (110 still is faster than others)

Cons
Is able to get countered if rooted or stunned because he is very slow
His E does practically no damage is only a good root
W move explodes on almost everything: Turrets, broken turrets, inhibitors,
broken inhibitors, walls, and enemy champions

His W move is good for stunning in a team fight. His E does nothing, but can root during a team fight. In a small groups you should use W and then your ult to do a whole bunch of damage. His ult is very good in a team fight and can possibly get you a penta-kill if you play your combos correctly.