The characteristics of the Greek vocabulary is an issue for which we could write volumes. It is difficult and a little "dangerous" to touch it superficially. What comes to mind and what I discuss most often with my students are the following:
One of the most characteristic features is the intense "multi-sense", that is, the many different meanings that one word may have.
Example: λόγος : speech, ratio, reason, cause.
Also, the ability of the language to combine many prefixes with one word and to create many words which have new meanings.
πρόλογος (προ + λόγος) : preface, introduction.
επίλογος (επί + λόγος) : epilogue.
These characteristics, which, of course, exist to a greater or lesser extent in all languages, make Greek a particularly rich and creative language.
Another feature is the variety of endings of the same word, due to the inclinations in Greek. Each noun or adjective depending on its position and its syntactic role within the sentence can take 4 different forms in the singular and 4 in the plural.
ο μαθητής διαβάζει = the student is studying (Nominative)
το βιβλίο του μαθητή = the student's book (Genitive)
ακούω τον μαθητή = I am listening to the student (Accusative)
μαθητή, έλα! = student, come! (Vocative)
Οι μαθητές διαβάζουν = The students are studying. (Nominative)
τα βιβλία των μαθητών = the students books (Genitive)
ακούω τους μαθητές = I am listening to the student (Accusative)
μαθητές, ελάτε! =students , come! (Vocative)
These grammatical forms are called “cases”and are often a headache for students. Cases, of course, were originally characteristic of all the Indo-European languages family. Depending on the evolution of each language, some have maintained them (ex: in Greek) and other languages have dropped them (ex: in English).
Finally, Greek learners are impressed by the fact that very many words - terms of medicine, physics, astronomy, and many other sciences internationally - are Greek. This shows the contribution of ancient Greek philosophy to the consolidation of modern sciences.
αστροφυσική : astrophysics
γαστροσκόπηση : gastroscopy
αμφίβιος : amphibious
αρχαιολογία : archaeology