| How do I file the NY State taxes?
Your CPA will file a multi-state individual tax return that would include both a California and NY State Individual Tax Return. So, he will know what to do!
Am I liable to pay taxes for the full year's wages though I never earned them in NY?
No, you are not liable for taxes that are due on Wages earned in California.
How do I report the wages I actually earned in NY when it is not mentioned on the W-2?
But, you mentioned that "For NY it shows the total Federal wages along with corresponding taxes withheld for the 1.5 mths I worked there." This is the income that is to be sourced to NY. In fact, your W-2 would show an amount sourced to New York State. | 
