I would say that, whereas Romans 13 is definitely political (and pro-Roman), the statements about the "world" in both John and James have little if anything to do with politics. As far as the Gospel and epistles of John are concerned, I think Gumby points to the right direction in referring to Gnosticism. In the Fourth Gospel the world (kosmos) is systematically opposed to the "above" Christ and his followers come from (8:23; 13:1; 14:17ff; 15:18f; 16:28; 17:6,9,14ff; 18:36; 1 John 2:15ff; 3:1,13; 4:3ff,17; 5:19). "The Jews" otoh belong to the "world," and "the ruler of the world" is opposed to "the Father" (12:31; 14:30; 16:11). Those lines will be hardened in later Gnosticism where the OT God will be clearly identified to the "ruler of the world". In James the "world" is used in a similarly religious yet more ethical way, as applied to communitarian behaviour (which should not resemble "the world," 1:27; 4:4). This is hardly related to politics either.
As a side note, whether Paul was beheaded or not rests on the appraisal of later Christian tradition. The book of Acts (which is heavily pro-Roman, blaming Paul's troubles on the Jews and even Jewish "Christians," cf. chapter 21), does not record his end.