You can't claim your NY expenses - sorry. I assume that since you work in NY five days a week, NY is now your principal residence (for tax purposes) and Ohio is your 2nd home. What you can do is deduct moving expenses - one time travel expenses from Ohio to NY, plus costs of moving personal possessions to NY. See Pub 521 for details:
Publication 521 (2008), Moving Expenses You can not claim your regular travel expenses to go back and forth to Ohio, as this travel is not required by your employer.