You have asked a very interesting question. When we construct a sentence, we may be confused about the order of word classes in a sentence.
Your sentence: "Greet politely and kindly the students" sounds unnatural to the native speaker. In my opinion, your main emphasis is on the act of greeting students. Therefore, it would be clearer to keep "Greet" and "students" together, and group the adverbs together behind to provide more information about the manner in which you greet them:
Greet the students politely and kindly.
Take another example:
Board quickly the bus. vs Board the bus quickly. (The latter is very clear as you emphasise the type of vehicle you board. Quickly describes the manner in which you board.)
I tried my best to provide my opinion. Do let me know if you still have doubts.