English: He "gives off" a strange vibe. Español: Él se "desprende" extraño.
It is closer to "give away" In your example, give off, could be translated to "emana" o "genera" English: He gives off a strange vibe. Español: Él emana/genera una extraña influencia/sensación (note: added a suggested translation for vibe, although it is slang, so could be localized and have many options for translation)
You could think that "desprender" is a more conscious act, like "give away" that you chose when to do, while "give off" can happen any time.
"Desprender" is a verb indicating something is getting separated from something else, so it is technically correct, but not close to what the English phrase meant.