Надо и нужно

Надо means I must, I should, I need to - with a moral like obligation implied: 

"I need to call my mom."

 

Нужно is a more straightforward need without moral obligation implied: 

"I need a pencil for this task."

Надо is a more informal, colloquial form

My native friend said that there's no real difference between надо and нужно. His words: Usually we don't put nouns after "надо" like, say: "мне надо такси". It sounds much better if you use it with the verbs: "Мне надо вызвать такси". "Нужно" is also used exclusively with verbs, but you can use it with nouns IF you modify this word according to genders: 

 

Мне нужен телефон - I need a phone 

Мне нужна ручка - I need a pen 

Мне нужны деньги - I need money 

Ты мне нужен – I need you