(archaic) Insincere or nonsense speech. This term is an example of 1920s ("flapper" era)American slang. Synonyms from the era include horse feathers and applesauce.
"He poured banana oil in her ear, telling her flattering sweet lies to lure her heart."
an unbelievable justification for getting someone totally screwed
He started up a successful banana oil business in Siberia, Russia whilst Mr Putin was in power