For the West Indies this was a second comprehensive defeat in as many days after their 103-run reverse against reigning champions Australia and now the hosts face a major struggle to qualify for the semi-finals.
Chasing 178 to win, New Zealand finished on 179 for three with more than 10 overs to spare.
Styris was 80 not out - his third fifty of this tournament - with Craig McMillan unbeaten on 33 as the experienced duo shared an unbroken fourth-wicket stand of 102.
Victory had been all but assured by a disciplined bowling display that saw New Zealand dismiss the West Indies for 177 with 32 balls left in the innings.
Oram took three for 23, his treble behind a slump that saw three top-order wickets lost for 15 runs in six overs.
Fast bowler Shane Bond had three for 31 and left-arm spinner Daniel Vettori, who late on took two wickets in two balls, finished with three for 39.
Impressive wicket-keeper Brendon McCullum led a fine fielding effort with four catches.
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