"when you are done" vs. "when you are through" vs. "when you are finished"

Hmm.

"When you are done cooking" sounds a bit suss compared to "When you are finished cooking", although I can't quite pin down why. "When you are done with cooking." sounds a bit better.

I think this usage of 'through' is quite American, but I'm not certain. It's certainly not common in Australia!

Summed up, "I am done" and "I am finished" and "I am through" are all correct, if used in the appropriate context.

Explaining why:

I've always been brought up to the idea that "done" is used for objects i.e. Cooking is done, or work is done, and "finished" is used for people, i.e. I have finished.

"I am done" implies that you have been worked upon, which obviously is not what you are trying to communicate. Rather, you are trying to say that you have finished doing. It is correct to say "I do", and "I did", but "I am done" is informal. The reason for its popularity and common use is due to its close affinity with "I do" and "I did" and people assume that "I am done" can be used.

"I am through" is sometimes colloquialism; it means that you have completed, and is correctly used in certain cases, as in " I am through the course", but usages like "I am through with you", is derived from "I am through the course", and is informal. It's not standard, but its commonly used. "I am through" is also used informally in cases like "I am through with this job".