Hi,
I've lived in Ohio last year, but my pay roll has been running from California state, so now I've to pay the Ohio taxes and get a refund from California.
FOR California there is an SUI/SDI tax.
How do I get the refund for SUI/SDI taxes from California?

Contact the California Franchise Tax Board (you can get the phone number from their website).

You clearly are NOT liable for these taxes, and they will tell you what form to submit to request a refund.