Could Have / Must Have / Should Have Would Have / Might Have

Could Have/ Might Have + V3

They mean to say that if we had wanted something in the past, we had had the opportunity to do it.

- I could have moved out when I was 18, but I didn't want to leave my family.
 (I chose to stay)

- I might have moved out, but I didn't want to leave my family. 
(I chose to stay)

- I could have gone out with my friends but I wanted to watch the soccer game. 
(I could but I didn't go with them)

- I might have gone out with my friends but I wanted to watch the soccer game. 

In both sentences, either action was possible for me but I stayed home to watch the game, 
I may be watching the game at the moment while my friends are out or perhaps this was yesterday.

Should Have V3 / Ought to Have V3

It was in the past, and that we didn't do something we were supposed to do. It was a mistake.

- You should have checked your answers thoroughly before you handed in your exam. 
(but you didn't which was a mistake)

- You ought to have checked. (Same but stronger than should have)

- You ----- asked my permission before you used my computer. I’m really angry with you.

a)needn’t have

b)should have
c)ought to have

- You ----- watching TV all night yesterday, that’s why you feel so tired now.

a)should have

b)ought to be

c)should have been

d)ought to have been

e)shouldn’t have been

f)ought to not have been

g)should be

h)ought not to have

i)ought to

j)ought not to have been 

Must Have / Would Have

Referring to past events. Must have + V3 is when we talk about our strong opinions based on evidences / facts.

- Do you know Ryan's math grade?

- I don't know but he must have got an A. (His math is really good)

Would have + V3 is similar to could have and might have but would have is more about
something we chose to do or not to do in the past because a certain necessity
was not met. Something was missing and that we chose to do what we did and that would
have is usually combined with if clauses.

I would have moved out but I hadn't had enough money.

(I wanted to move out but I didn't have money)

I would have been smiling if you had brought me some flowers. 

(You didn't bring me flowers, so I am not smiling)

I would have never divorced him if he hadn't hit me.

(I would never divorce him unless he hit me. / He hit me, I divorced him) 

Couldn't Have + V3

It means to say that in the past even if we had wanted something, we didn’t have the chance 
to do it.

- I couldn't have visited you when I was in Paris as I didn't know your address.

(I didn't visit you when I was in England but it was not possible anyway)

Negative Modals + V3 Table

Can’t Have / Couldn’t Have V3	99% (impossibility)	I am sure he wasn't lying, he can't have cheated on you.
Mustn’t have + V3	85% (it can be wrong)	I can't believe him, he mustn't have crashed. Jerry was probably joking.
May / Might not have V3	50% (probably didn’t happen)	I am so curious, she may have won the contest, you never know.

Examples

One of them ---- be lying and I suspect it’s Emma.

a)must   b)may   c)must have   d)can’t   e)mustn’t

- When did you go shopping last?

- It ---- ages ago.

a)must be -  b)may be   c)must have been   d)could be

Jane ----- about the meeting as she didn’t mention about it at all.

a)must hear

b)must have heard

c)can’t have heard
d)couldn’t have heard

e)needn’t have heard f)was able to hear 

http://www.grammarbank.com/could-should-would-must-have.html