pick up has 29 distinct synonyms spread across 10 of its 16 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.
take up by hand
“He picked up the book and started to read”
give a passenger or a hitchhiker a lift
“We picked up a hitchhiker on the highway”
get in addition, as an increase
“The candidate picked up thousands of votes after his visit to the nursing home”
buy casually or spontaneously
“I picked up some food for a snack”
lift out or reflect from a background
“The scarf picks up the color of the skirt”
meet someone for sexual purposes
“he always tries to pick up girls in bars”
fill with high spirits; fill with optimism
“Music can uplift your spirits”
improve significantly; go from bad to good
“Her performance in school picked up”
gain or regain energy
“I picked up after a nap”
Synonyms, antonyms and the broader and narrower relations for pick up come from Princeton University’s WordNet. Full sources and licences.