Is it permissible to swear an oath about something that occurred in one's imagination, such as saying: "By Allah, I went to so-and-so," while intending that this happened in their imagination?

The validity of an oath depends on the intention of the swearer. If the swearer intends a meaning for their oath that the word can bear, then their oath is directed to that meaning, whether the meaning aligns with the apparent meaning of the word or contradicts it. Ta'wiyah (figurative speech) or ma'arid (allusions) occur when a word has two meanings: a close one and a distant one, and the speaker intends the distant meaning. So, if the swearer says, "By Allah, I went to so-and-so," intending in their mind that this happened in their imagination and they did not actually go, they are not considered a liar.