World oil prices eased further on Tuesday, trading below 124 dollars a barrel as a firmer dollar encouraged profit-taking in a market that remains well-supported, analysts said.  New York's main oil futures contract, light sweet crude for June delivery, was 37 cents lower at 123.86 dollars from 124.23 dollars at the close of trading in New York on Monday.  The benchmark contract traded lower for most of the New York session, but struck a record intraday high of 126.40 dollars. Brent North Sea crude for June delivery was 14 cents lower at 122.77 dollars a barrel after a drop of 2.49 dollars to 122.91 dollars on Monday.