The word "imk" appears to be a typographical error or abbreviation rather than a recognized English word. It could potentially stand for "I’m okay" in some informal online contexts. However, without further context, it's hard to define its meaning precisely.
Since "imk" does not have a standard meaning in English, we cannot trace a formal etymology. If interpreted as an abbreviation, it likely stems from informal texting conventions.
(Note: The examples demonstrate how "imk" might be used informally and conversationally if it means "in my knowledge" or "I’m okay.")