[III] - I ate the pie, and since then I have had a stomach ache.
I think this is the most natural comma placement: it divides the two independent clauses, which is what commas do.
I don't know who wrote your Sentence I (SI). To me, putting the two commas here is unnatural. It represents to me an unnatural way of expression. It also means there are two pauses within five words and two pauses in a straightforward sentence of 13 words. I don't know why anyone would want to slow down that much.
The two commas in SII make sense, because they separate a unitary phrase (since then) from the rest. But although this two-comma version works much better than SI, it's not as eloquently simple and natural as SIII. This is because SII also introduces an unneeded double pause in a thirteen-word sentence that needs, at most, one pause. (Note that my use of commas to separate at most is similar to II's comma use.)
You could also dispense with the 'since then' and write the remaining with either no comma or one comma:
[SIV] I ate the pie and I have had a stomach ache.
To me this expresses both thoughts as one unit containing two facts. It does not really stress a causal or resultative relationship between the two actions/facts. Also a comma is just plain unnecessary because now the sentence is unencumbered by the 'since then', and it has only eleven words. I mean it is short and consists of two short independent clauses.
[SV] I ate the pie, and I have a stomach ache.
This goes back to the simple connection of the two independent clauses with a comma immediately after the conjunction, as in SIII. This is very frequently done, and at least helps the reader parse the sentence if not also slow down a tiny bit. (See how I used only one comma in that last sentence, and only to separate the two clauses? Oops, I just did it again.) SV probably does not present the two actions in terms of one unit of dual-facts like SIV. Perhaps because the pause also allows a millisecond for the reader to make some causal or resultative assumption between the two clauses--even though the comma by itself does not do that.
Best Answer
As in many languages, in English, commas represent the pauses that a speaker would include when saying the sentence out loud. In this way it mirrors the natural rhythm of the language, which varies considerably between different dialects and different individuals.
So most rules that seem to require commas before or after certain words or phrases are simply guidelines to help you organize your English sentences. It's a good idea to learn these guidelines, and understand what purpose they serve, but then pay attention to how native speakers talk and write, and develop your own personal style.
That being said: words like "tomorrow" and "yesterday" may be followed by a comma if you wish to help separate it from the next word or phrase in the sentence. Sometimes this helps understand the sentence better:
The comma helps separate the ending "y" of "someday" and the starting "y" of "you" in the same way that a speaker might insert a pause there. The comma is not necessary, and it does not change the meaning of the sentence, but it does change the rhythm of the sentence to mimic natural speech patterns.