Do we still use the term "astronomical unit" nowadays? An astronomical unit is defined as the measurement of distance between Earth and our Sun, my question is since distances between celestial objects beyond our solar system are vast and unimaginable astronomer adopted another familiar term "light-year" instead. My question is do people still use astronomical unit in the present days?
Certainly. Astronomical Unit is probably one of the most used distance units used in astronomy. It is of course only used when discussing the distances within a stellar system, such as the distances between the Sun and its planets or other bodies in the solar system. It is also used to discuss distances in other stellar systems, e.g. the distances between stars and their (exo)planets.

It is easier to get a sense of the distances between bodies in the solar system if you use astronomical units. It doesn't say much when we say that the distance between Neptune and the Sun is $5\times10^{-4}$ light year. You would have to know the distance between Earth and the Sun ($1.5\times10^{-5}$ light year), and then calculate the difference (i.e. 30 times = 30AU) to get a sense of scale.

As a side note, in professional astronomy, the light year is hardly ever used. Professional astronomers use the parsec (=3.26 light year), kilo parsec (kpc), megaparsec (Mpc), and Gigaparsec (Gpc) to specify distances between stars, galaxies, and galaxy clusters.