1. He was sick so he couldn't go to work.

2. He was sick, so he couldn't go to work.

3. He was sick so that he couldn't go to work.

(What is the difference among them? Does #1 mean #2 or #3? What is the meaning of #1?)

Number 1 is correct; a comma is not needed. He was sick so he couldn't go to work.

Number 3 -- omit "that."

The three sentences have slightly different meanings and nuances.

1. "He was sick so he couldn't go to work."
In this sentence, the word "so" is used as a conjunction that indicates cause and effect. It means that because he was sick, he was unable to go to work. It implies a direct cause and effect relationship between being sick and not being able to go to work.

2. "He was sick, so he couldn't go to work."
This sentence is similar to the first one, but it uses a comma to separate the clauses. The comma serves to make a slight pause in the sentence and emphasizes the causal relationship between being sick and not going to work.

3. "He was sick so that he couldn't go to work."
This sentence introduces a different nuance. The word "that" suggests a purpose or intention. It implies that being sick was intentional or planned, probably as a means of avoiding going to work. The use of "couldn't" instead of "can't" indicates that the person deliberately made it impossible to go to work.

In summary, #1 and #2 have similar meanings and imply a direct cause and effect relationship. #3 suggests intentional or planned sickness to avoid going to work.