"We ask them what they want."
Translation:אנחנו שואלים אותם מה הם רוצים.
They're similar enough that you won't be wrong in using any of them in any situation.
The word על is most common, while אודות is slightly more literary, but it's common to see "אודות החברה" or "אודותינו" on corporate websites where "about us" would be in English. The last one, בעניין, is kind of slangy, because the word עניין (matter) can be used as a stand-in for anything.
That vs What ש vs מה
The pronoun "that" precedes a statement of fact, which you may think is true or false. The Hebrew equivalent is the word אשר, or its short form - the prefix ש.
The pronoun "what" precedes a pronoun clause, which takes the place of the noun. In this case the noun is a question - the question that we asked them. The Hebrew equivalent is מה.