1. to pull shut (For a sliding door, curtains or a noose.)
2. to move somewhere (Has the vibe of moving into an existing community. Only used in formal contexts. The noun and adjective "zugezogen" are more common than the verb (and still rare).)
3. to get cloudy ("sich+Acc zuziehen" - for the sky getting overcast.)
4. to incur, to sustain ("sich+Dat etwas zuziehen" - Mainly used for injuries. Not common at all.)