There are really three different verbs.
1    should
This verb (/ should/you should/he should etc) is used to talk about obligation, and in some other ways.

2    would
This verb (/ would/you would/he would etc) can be used to talk about past habits, and to make polite requests.

3    should/would
This verb — the conditional auxiliary — has the following forms:/ should/would you would he/she/it would we should/would they would

The conditional is used in sentences with if, and in some other ways.

We can ask a question beginning Why should . . . ? to show that we do not understand something.

• Why should it get colder when you go up a mountain? You're getting nearer the sun.
  

Why should I? and How should I know? show that we are angry.

• 'Give me a cigarette.' Why should I?'
  
• 'What's Susan's phone number?' How should I know?'