In the 1940s, Army Street (renamed Cesar Chavez in 1995) was more than doubled in width. As a result many of the houses and buildings on the north side of the street were torn down. However, some were moved.
The apartment building at 3365 Cesar Chavez was once 3370 Army. Why would an address change from an even to an odd number? Because at some point in the 1940s it was moved across the street and rotated, which explains its jaunty angle.