Here the first use of the word "they" as well as the words "their" and "them" refer to Paul and Silas. Compare [Acts 16:25](./25.md). The last use of the word "they" refers to the people in the jailers' household.
The words "him," "his," and "he" refer to the jailer.
Here "word" stands for a message. Alternate translation: "They told him the message about the Lord Jesus" (See: [[rc://en/ta/man/translate/figs-metonymy]])