Hello!
I worked in Ohio until May 2009 and moved to CA for a new job since then.
1. How should I prepare Federal Income Tax Return and which form should I use?
2. New company reimbursed some part of moving expenses, but I can claim separate itemized deduction. What other deductions can claim in my case other than moving expense?
3. State Income Tax Refund: I can efile for Ohio tax turn, but how can I do CA tax return? Same online for CA tax?
4. In Ohio, there are different tax ratio for each city. How about CA city tax? What is CA SUI/SDI tax? I worked in Santa Barbara and Lompoc in 2009.

I appreciate your consultation in my case,

Karen

Income earned while in CA must be reported to CA. You are part year resident of CA. Same treatment for Ohio.
CA does not have city tax. You do not report CA SDI on your tax return. This is disability insurance payment.