Here's a quick and dirty explanation, couched in non-technical terms. Let's assume you are speaking each sentence in the year 2013. In 1a, then, [I have lived in Paris for 4 years] the implication is
Either you have lived elsewhere prior to 2009, or someone asked you in 2013 "Where have you lived previously?" or "Tell me about the places you've lived since 1998?"
Number 1b [I have been living in Paris for 4 years] could be an answer to the question
"Where have you lived since 2009?" or "How long have you been living in France?"
Number 2a [I lived in Paris for 4 years] describes
A person who has lived in two or more locations prior to 2013, and one location happens to be Paris.
Number 2b [I had lived in Paris for 4 years] begs to be followed up with, for example,
". . . when I realized I could live there no longer."
Similarly, 3a [ I had lived in Paris for 4 years] begs the question
"What happened after you had lived in Paris for four years?" and you say, "Well, after I had lived in Paris for 4 years, I decided to stay another 4 years."
Number 3b [I had been living in Paris for 4 years] could be followed up with
". . . when I realized I would live there the rest of my life," or ". . . when I decided to move to Florence."