His son was slugging along with the work.
Have you heard of this expression?
I know the word 'slug' means either a snail without a shell or to hit something very hard.
I think it means his son was lazy or sluggish in doing his work but I've never found this expression on google.
If I used this in America, would people even understand?

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Hello!

To "slug something out" also means to keep on going until the person has won or achieved their goal.   So to say "His son was slugging along with the work" probably means that his son was working hard and just kept on going until the work/job was completed.

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Perhaps you mean to say "slogging along"? Meaning, to work hard continuously over a long period of time. "Slugging along" would change the meaning.

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Sluggish is an adjective. It means slow-moving, lacking in energy. Similar to how humans perceive slugs!

To slug something, the verb, means to take a big drink of (usually) alcohol: "he slugged the beer". Slugging would be the gerund and past participle.

Without a broader context, I am not certain whether the son was 'slugging (beer) along with the work' or if the son was being sluggish about the work. Though I suspect it relates to being lazy and slow in relation to the work he has been given.