The correct sentences are The lead actor's ad-libbing was completely beyond the pale and The director resigned under a cloud of suspicion after the disastrous opening night.

Idiom Breakdown:

• Beyond the pale uses the preposition beyond and means unacceptable or outside agreed standards of decency.

• Under a cloud uses the preposition under and means suspected of having done something wrong.

• The incorrect idiom on the offing should be in the offing (meaning likely to happen soon).

• The incorrect idiom against odds with is a mix-up; it should be at odds with (meaning in conflict or disagreement).