What era spans from 1945 to the present ? the classical era, the modern era, the contemporary era, or the early modern era

The present ere is the "contemporary" era.  You and I are contemporaries because we're living at the same time.  So from 1945 (after World War II) to the present can be referred to as the contemporary era.

The "classical era" could refer to the time of ancient Greece and Rome ... or if you're talking about music, the classical period spanned from early 1700s to early 1800s.

The "modern era" in history was introduced by the Scientific Revolution and the Enlightenment, so from around 1500 to early 1800s.  The "early modern era" would be the beginning of the modern era, with thinkers like Francis Bacon and Rene Descartes sending intellectual history in a new direction.