What is the difference in usage between the pairs 依然/仍然 and 依旧/仍旧?
仍旧 means 'still (as always/ same as the past)'
依旧/仍旧 is more specific term for 'still'. It express something 'stay the same despite passing of time '

Example 1 : 五十年过去了, 他仍旧住在那条街上 (fifty years is a long time)
Example 2 : 三年过去了, 我仍旧相信他是无辜的 (three years have passed, nothing changed, I still believe he is innocent)

仍然 means 'still (despite of)'
依然/仍然 is more general term for 'still'. It express something 'stay the same despite any opposing force or reason'

Example 3 : 五十年过去了, 他仍然住在那条街上 (despite the fact that many things would had been changed in 50 years)
Example 4 : 尽管有这么多证据,我仍然相信他是无辜的 (despite the fact that all the evidences are against him, I still believe he is innocent)


*仍旧/依旧 is actually a shortened form of 依然如旧 / 仍然如旧(still like always/ still like before/ still like in the past)

Although they can be used interchangeably sometimes, they are not synonyms.