How's everyone spending your New Year?
While you would say "(I'm) okay," "(I'm) fine," "(I'm) good," and --- "(I'm) great," in response to, "How are you?," would you say, "I'm okay," or, "I'm great," to, "Would you like something to drink?" at somebody's home or on board a plane?
Also, when you have tripped over, and someone has asked you, "Are you okay?," would you say, "I'm good," or, "I'm great"?
Hiro/ Sendai, Japan
I think it depends very much on which English-speaking community you are living amongst, and to some extent on their age group.

For example, people over a certain age (in the UK, where I live) are not likely to say "I'm good" in response to the question "How are you?"; they are more likely to say "I'm fine, thanks". For now, at least, "I'm good" is more the province of the young in the UK.

In response to the question "Would you like something to drink?", I'd be very unlikely to "I'm great" in response, although I might well say "No. I'm fine, thanks", or "No, I'm okay thanks!"

As for "Are you okay?" in your example above, no, I wouldn't say "I'm good" or "I'm great"; I'd say "Yes, I'm fine thanks!".

However, Americans, Australians and other native English speakers, might well give different answers to mine.
What about "I'm great" to the question "How are you?" in the UK? Assuming from "I'm good," I guess you would much more unlikely use it than "I'm good."
Hiro/ Sendai, Japan
Students: Are you brave enough to let our tutors analyse your pronunciation?
I might say, "I'm feeling great, thanks!", but I wouldn't say a stark "I'm great!". I'm just as likely to say "I'm very well, thanks!", but these kind of responses are sometimes very individual, and depend upon the age and personality of the speaker, and, as I mentioned above, on whatever English-speaking community you happen to be living in.
I'm interested to know how the questions would be answered elsewhere and in different generations. Having stayed in the U.S. for quite some time in the past, I'm too used to the reply "Good" in response to "How are you?"

Hiro/ Sendai, Japan