What is being said:
Q: Do you want a hotdog?
A1: I'm okay/That's okay. Thanks.
A2: I'm good/I'm cool/I'm fine.
A3. That's OK. Thanks
What isn't being said, but might be implied:
Q: Do you want to change your present situation by adding a hotdog to it?
A1: I'm okay the way I am. Thank you for offering to give me a hot dog.
A2: My present situation is good/cool/fine.
Note that all of these responses (I'm okay, I'm good, I'm fine, I'm cool) are casual speech, to varying degrees. I would use them with my friends, or my employer, but maybe not with my prospective employer. For example, in a job interview, I might say I'm fine, thank you but not I'm cool, thank you. If the president offered me the hotdog, I would either just say No thank you, or, most likely, accept the hot dog.
Note: This usage of I'm OK is fairly common in the U.S. (At least on the west coast.) To my ear, it is virtually interchangeable with "That's OK." @DavidRicherby indicates in the comments above and below that "I'm OK" is used in British English, but "That's OK" is not (at least not in this sense.)