Can I use "or" between two synonyms?

Yes. What you have written is grammatically correct. Even the closet synonyms can convey subtly different meanings. Thus, combining them, as you have done, can more accurately capture what you wish to convey and add clarity for the reader.

I would add that 'paradigm' and 'style' are not necessarily synonyms. 'Paradigm' has the sense of a viewpoint that is shared by a cohort whereas 'style' is more individual. Using both gives the sense that one can follow a certain prescribed approach in their writing of Java code whilst still retaining some individuality of expression. If that is your intention then you have achieved it.