Unionized nurses and management at Saint Vincent Hospital in Worcester agreed to a new three-year contract yesterday, averting a strike that had been called for tomorrow. Yesterday's deal increases the pressure on Tufts Medical Center in Boston, where management and the nurses union plan to resume contract talks today in a last-ditch effort to prevent a strike there tomorrow. Talks at both hospitals, and at others across the state and nation, have centered on staffing levels. The parties at Saint Vincent, who had been negotiating on and off for nearly a year and a half, reached a settlement after a six-hour bargaining session. Under the new contract, patient ratios will be reduced to four to five per nurse on the day and evening shifts, and no more than five on the night shift. Patient ratios are currently up to six on days and evenings and up to seven at nights.