Usually 一番／最も良い and 一番／最も悪い would be good semantic counterparts of best and worst in English, respectively. The words you mentioned all have extra connotations when they seem to translate "best" or "worst".
This word literally means (as a superlative) just "lowest", as in 最低気温 "lowest temperature" or 最低賃金 "lowest (=minimal) wage". It however has another mostly colloquial meaning that is "base, low" as in "low deed". In this meaning it's no longer a superlative, which is proven by the fact you can add another 一番 before it.
the lowest man (= the biggest jerk = the worst man) I've ever seen
The slang usage is often shown in katakana (サイテー).
The literal meaning is "highest" or "supreme", as in 最高裁判所 "Supreme Court". This word also has a colloquial meaning that translates into "great feeling, fantastic, on the top of the world" etc., that could be reworded as "best", could be written サイコー, and accepts an extra 一番 as well.
Their food is awesome (= superb = the best)!
Its exact nuance in ordinary meaning is something like "most unwanted", as in 最悪の事態 "worst case". Again, the second meaning: "(felt) awful, annoying, terrible", also written サイアク, and yes, you can say 一番最悪 too. So in this sense, 最悪 and 最高 make antonyms.
At worst, we will have to escape the Earth.
The most terrible (= the worst) mistake since the beginning of this year
It is simply the antonym of 最悪's non-slang meaning, that is "most satisfactory, optimal". This one has no other meaning, but is a relatively bookish word. You'll often find another word 最善, which means "the best possible", more useful than this.