bag has 15 distinct synonyms spread across 9 of its 14 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.
the quantity of game taken in a particular period (usually by one person)
“his bag included two deer”
a place that the runner must touch before scoring
“he scrambled to get back to the bag”
a container used for carrying money and small personal items or accessories (especially by women)
“she reached into her bag and found a comb”
the quantity that a bag will hold
“he ate a large bag of popcorn”
a portable rectangular container for carrying clothes
“he carried his small bag onto the plane with him”
an ugly or ill-tempered woman
“he was romancing the old bag for her money”
an activity that you like or at which you are superior
“chemistry is not my cup of tea”
capture or kill, as in hunting
“bag a few pheasants”
bulge out; form a bulge outward, or be so full as to appear to bulge
Synonyms, antonyms and the broader and narrower relations for bag come from Princeton University’s WordNet. Full sources and licences.