awkwardness has 10 distinct synonyms spread across 5 of its 5 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. Its one recorded opposite is gracefulness.
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.
unskillfulness resulting from a lack of training
the quality of an embarrassing situation
“he sensed the awkwardness of his proposal”
the carriage of someone whose movements and posture are ungainly or inelegant
the inelegance of someone stiff and unrelaxed (as by embarrassment)
trouble in carrying or managing caused by bulk or shape
“the movers cursed the unwieldiness of the big piano”
Synonyms, antonyms and the broader and narrower relations for awkwardness come from Princeton University’s WordNet. Full sources and licences.