assignment has 6 distinct synonyms spread across 4 of its 6 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.
a duty that you are assigned to perform (especially in the armed forces)
“hazardous duty”
the instrument by which a claim or right or interest or property is transferred from one person to another
the act of distributing something to designated places or persons
“the first task is the assignment of an address to each datum”
(law) a transfer of property by deed of conveyance
an undertaking that you have been assigned to do (as by an instructor)
the act of putting a person into a non-elective position
“the appointment had to be approved by the whole committee”
Synonyms, antonyms and the broader and narrower relations for assignment come from Princeton University’s WordNet. Full sources and licences.