A website to help you study the Gospel of Luke,

He uses a large number of words we find nowhere else in the New Testament.

261 appear in the Gospel only
471 others appear only in Luke/Acts
Wherever he tells the same story as Matthew and Mark, in `almost every narrative' he changes words to use a classical expression which is better Greek.
He uses a large number of medical terms, as you'd expect from a doctor. This has been challenged (because almost all of the `medical' expressions in Luke can be found in other classical authors who weren't doctors); but to find all of those expressions in one place is significant! And when Luke describes a medical case, his words are always more careful and clinical than those of Mark and Matthew.
He uses lots of terms we also find in Paul; the impact of their working together is obvious!
He likes using compound words; he's fluent in Greek and confident in his use of it.
There are telltale stylistic marks which make his writing distinctive, including his use of the optative mood (which not many New Testament writers use); his heavy use of the conjunction te; and his fondness for de kai (which Paul also uses a lot!). These things make his books unmistakeable and give us total confidence that they were really written by the same author.
Curiously, though, there are lots of Hebraisms too - places where Greek is used in an odd way, as a non-Greek might speak it. It has been suggested that this is because Luke knew the Septuagint very well indeed (that's obvious from the use he makes of it in his writing) and so his whole style has become affected by it.
On the other hand, it's also been pointed out that Luke is fluent enough in his use of Greek to mimic the styles of other people where he wants to. We hear the real speaking voice of different groups of people in the Gospel, and especially in Acts.