What does I am all stomach mean?
A: ‘’It’s my turn for a gift. I would like to take you to lunch. To my favorite spot.’’
B: ‘’I am all stomach, professor!’’
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To a native English speaker, "I am all stomach" obviously references back to the phrase "I am all ears", which means "I am ready and eager to hear what you have to say".
This phrase would probably be interpreted to mean "I am ready and eager to eat what you are offering to feed me."
Additionally, as BlueRaja - Danny Pflughoeft commented below, this phrase is humorous and would likely be considered funny as it is hyperbole.
Even though it is humorous, the idea that the person is eager to eat would still be conveyed unless this were said in a sarcastic way.