I think you should go review the dictionary definitions of so, such that, and so that.
1a is not correct or natural. In 1, so is part of "so bad" and functions as an adverb; without the adjective it is not grammatical or clear what you're trying to say, because there isn't anything for so to modify.
1b is grammatically correct but does not sound very fluent or natural. "such that" expresses purpose or result, like "The horrors and brutality occurring within a country are such that the rest of the world cannot morally stand by." I guess you mean "the movie was the kind of movie that made me turn it off" but this does not sound like a natural phrasing.
In 2a, I think you are confused about the use of "so that" - it is normally used to express purpose, like "They turned up the lights so that we could see better." In your sentence, it sounds like he is intentionally singing badly to make people not like something.