しとられん means you can't do something or can't focus on something, because there is something more important. In this sentence, it says when ジョー comes, you can't do businesses anymore. Probably, ジョー is a person who interrupt the businesses.
~ ちゅうて means "(someone) says ~". ちゅうて comes right after the content of what they speak. In this context, 商人 said "あのジョーがくるとおちおち商売しとられん".
おびえとる mean fear/be afraid of. In this context, 商人 is afraid of ジョー.
By the way, they all are dialect spoken by west part of Japanese people. In standard Japanese しとられん is equivalent to してられない, ちゅうて is equivalent to と言って, おびえとるん is equivalent to おびえている.