difference in meaning between 'incredible' and 'implausible'

[Violino]

I've got two questions that's been confusing me for few days:

1. What's the difference between 'incredible' and 'implausible'? Or they're synonyms and I can use them by turns?

2. Which is correct: 'I don't have a clue' or 'I haven't a clue'?
Is it exactly the same as 'I have no idea' ?
And can I use both those sentences in formal situations?

[Mister Micawber]

.
1-- 'incredible' = unbelievable but 'implausible' = unlikely. 'Implausible' has a higher probability than 'incredible'.

2-- Both are fine and all three are synonymous. None are formal; all are conversational.
.
_________________
Canadian-American native speaker
who teaches English for a living at Mister Micawber's
ESL cafe: Interview with Mister Micawber