tug has 10 distinct synonyms spread across 4 of its 9 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. WordNet records no antonym for it — antonymy is a relation between word forms rather than concepts, so it is deliberately sparse.
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.
pull hard
“The prisoner tugged at the chains”
tow (a vessel) with a tug
“The tugboat tugged the freighter into the harbor”
move by pulling hard
“The horse finally tugged the cart out of the mud”
pull or strain hard at
“Each oar was tugged by several men”
struggle in opposition
“She tugged and wrestled with her conflicts”
Synonyms, antonyms and the broader and narrower relations for tug come from Princeton University’s WordNet. Full sources and licences.