WordNet records no synonym and no antonym for oat. It is the only member of each of its synsets, which is common for technical, taxonomic and single-sense vocabulary — there is no other English word that means the same thing. The broader and narrower terms below are the useful relations in that case.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
annual grass of Europe and North Africa; grains used as food and fodder (referred to primarily in the plural: `oats')
seed of the annual grass Avena sativa (spoken of primarily in the plural as `oats')
Synonyms, antonyms and the broader and narrower relations for oat come from Princeton University’s WordNet. Full sources and licences.