Writing "A , so B, so C..." for series of implications

Solution 1:

Chaining clauses together with so, as in your example

He is sick, so he is on leave, so you have to do his work, so you cannot leave now, so please let her know.

is not incorrect per se, but you should be aware that it gives the sentence a rhetorical resonance (look up anaphora) that you may not intend. It makes the sentence into a kind of litany, and as a consequence may sound overly dramatic.

Language is a tool, and the speaker or writer's task is to fit the words and style to the task at hand. Consider Twain's sardonic essay On Cooper's Prose Style, in which he says:

Style may be likened to an army, the author to its general, the book to the campaign. Some authors proportion an attacking force to the strength or weakness, the importance or unimportance, of the object to be attacked; but Cooper doesn't. It doesn't make any difference to Cooper whether the object of attack is a hundred thousand men or a cow; he hurls his entire force against it.

So consider how much force you want to use in making your statement. If you really do wish to dramatize the causality chain, by all means use anaphora. But if the sentence does not merit the extra rhetorical effect, you might consider recasting it.

Solution 2:

I don't think this is okay because there are many conjunctions to express the same idea of cause and result (e.g. as, since, because, etc.), which you could use to avoid the repetition of so. For example:

As he is sick and is on leave, you have to do his work and therefore cannot leave now.

Solution 3:

Using so like in the example sentence doesn't seem correct, to me.

I would rather re-write the sentence as follows:

He is sick, and he is on leave; therefore, you have to do his work, and you cannot leave now. Please let her know.