WordNet records no synonym and no antonym for strongman. 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.
a man who performs feats of strength at a fair or circus
a powerful political figure who rules by the exercise of force or violence
“he is determined to bring down the Iraqi strongman”
Synonyms, antonyms and the broader and narrower relations for strongman come from Princeton University’s WordNet. Full sources and licences.