One thing we can say that Elves probably
don't eat is mushrooms.
This comes from a passage omitted from the Druedain material in UT but given in
Of Dwarves and Men:
Quote:
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To the astonishment of Elves and other Men they ate funguses with pleasure ... the Eldar did not eat these things.
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Tolkien struck this passage out, noting that it was "too like Hobbits", so it's up to us to decide if this was also a rejection of Elves not eating mushrooms.
Note also that he said "Eldar", so the Avari possibly do eat them.