How should I phrase it:
This question has been asked at Stack Overflow.
This question has been asked on Stack Overflow.
Prepositions are tricky. You can put something in a book or read something in a newspaper, but you always put something on the internet or find something on a certain website. Unfortunately, I don't think there is a general rule that can be applied here, but when it comes to the internet and websites, "on" is the most common preposition.
The only time you might see "at" used is when describing the full URL for a website:
"At" tends to be used with specific locations, i.e. when something is at the top of the page, or at the end of an article.
I don't think "at StackOverflow" is wrong; that is, I don't think you must always say "on [some website name]". At can be used for fairly broad locations, such as "at home". However, I can think of one connotation of at that I don't think occurs with on, which is the distinction between related things with the same name.
That is, in the paper
This only makes sense for the website
This could be referring to the organization itself, e.g., the workplace, the company, etc. But if it's clear from the context that you are referring to the website, I don't think it's wrong to use "at website".
That sounds a lot better to me than "at SO" or "in SO".