We do enjoy this

Answer 3 is the strongest here; No.1 is unambiguous but very curt and simple, while No.2 does echo the form of the question (which No.4 does not: the 'do' auxiliary may be emphatic, but it doesn't match the question in the terms that it was asked).

Answer 2 is nicely-judged and balanced. Answer 1 is too abrupt, and Answer 3 doesn't offer any contradiction (the 'no', in context, is agreeing with the negative supposition in the question). Answer 4 is too flippant, confrontational and generally likely to get the meeting off to a nervous start.

'Me' (Answer 3) would be widely heard, yet 'me is coming' would plainly be ungrammatical. 'I am' contains the affirmative (and unabbreviated) echo of the verb from the original question. You would not use the shortened form (Answer 4) in an elided answer by itself; it looks pretty strange, and it would sound out of place, even though it would probably be understood.

The 'I do' form (Answer 1) was an older response to the formal question 'Do you take ... ?', but the form nowadays is usually 'I will'', which is clear enough in intent but also blurs the sense of future time with a sense of emotional commitment (willing the marriage to work).
'I must' is not very confidence-inspiring, and 'I shall' is almost too formal; besides, neither of them echoes the phrasing of the question.

Answer 1 strikes the best balance: it avoids the rhetorical question (Answer 2; however tempting and called-for that may seem, as a device to challenge the person you're talking to) and also the sarcasm in Answer 3. Answer 4 is too blunt and unhelpfully unspecific.

... And the word 'do' (Answer 3) was the first strong-beat word in the song ~ one of the best and most widespread (and indeed, one hopes, happiest) examples of 'do' as an Emphatic Auxiliary verb.
None of the other paraphrases has anything like the rhythmic vigour or rhetorical force of the correct version. You may like to try Googling it!

It should strictly have been 'definitely not I', but very few people are pedantic enough to bother about that these days; Answer 4 is the best polite option here.

Answer 1 is a simple instruction; Answers 3 and 4 are critical in tone, and sound as though they're being spoken afterwards, by which time it's too late (perhaps they're complaining at having to drive out privately and rescue a fried or relative that was too selfish to have planned sensibly ahead).
The version in Answer 2 manages to build-in both a sense of recommendation, and personal fellow-feeling (as though to say, 'you can believe this from me: I was once foolish enough to have had that experience myself, and heartily suggest you avoid doing the same').

Answer 2 uses the quite emphatic 'whatever?' and also refers to an individual who may be in some kind of trouble (ill, drunk etc.) rather than a more general enquiry.

These are all pretty clear and categorical, but they vary quite widely in 'tone'.
Answer 1 sounds like an uncle or grandparent warning a naughty / inquisitive younger member of the family; Answer 3 also sounds strangely personal, but the version in Answer 4 might perhaps be seen on a temporary sign (perhaps while heavy maintenance is being done, e.g. on the central boiler). The wording in Answer 2 is nonetheless stronger.