eke out has 2 distinct synonyms spread across 3 of its 4 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.
supplement what is thought to be deficient
“He eked out his meager pay by giving private lessons”
live from day to day, as with some hardship
“He eked out his years in great poverty”
Synonyms, antonyms and the broader and narrower relations for eke out come from Princeton University’s WordNet. Full sources and licences.
make by laborious and precarious means
“He eked out a living as a painter”
obtain with difficulty
“He eked out some information from the archives”