Northeastern International Airways suspended service on all but one of its routes after an unsuccessful attempt to attract passengers with new cut-rate fares. The airline, which filed for bankruptcy Tuesday, suspended ''until further notice'' flights to Chicago, Philadelphia and Orlando, St. Petersburg and West Palm Beach, Fla., a spokesman said. It is continuing flights between Islip, N.Y., and Ft. Lauderdale. A Northeastern flight from Chicago to Florida was canceled Wednesday because of mechanical problems. The privately held Ft. Lauderdale-based airline owes some $15 million to creditors. Under mounting pressure from creditors, Northeastern terminated flights to a number of cities earlier this week. The operation was undercapitalized and ran into problems after a quick expansion.