Firstly, about me:
I am an Indian citizen
Came to US on F1 in 2002
Always been a resident of California
Was filing 1040-NR-EZ, 8843 and CA-540-2EZ

But,
I am now on H1B visa since Oct 1st, 2006
I got to know that I am still a non-resident for 2006 tax year
So, I have to file 1040NR or EZ and can use the standard deduction of $5150 + $3300 exemption. Correct me if I am wrong here.

Now the problem: STATE TAX
Although I worked in California, the company who did my H1B is in NJ and their W2 has NJ in column 15 (State) with state tax, SUI and SDI paid to NJ.
I also have another W2 from another company for which I worked on OPT from Jan to May 2006. That's from CA and no worries there with only federal and state tax withheld.

I heard from some sources that I should continue to file CA-540-2EZ and include both the earnings of CA and NJ companies since I was in CA and also file NJ state tax as a non-resident (NJ 1040NR)

I do not have to include CA earnings in the NJ state tax form. But, in the form CA-540-2ez, should I also include the NJ state tax withheld while answering the question of total state tax withheld?

And what about the SUI and SDI I paid to NJ? Can I get a refund?

Also, only the NJ company has withheld social-security and medicare tax since I was on H1 with them. But, since I am filing as a non-resident for federal tax, can I ask a refund of it? If so, how?

Please help me here.

Yes, you can STILL claim the $5,150 standard deduction.

You must claim ALL income on the California return, and only NJ income in the NJ tax return. You will get ALL of your NJ withheld taxes back, as NJ has no legal standing to impose taxes on income NOT EARNED in NJ.

You will have to contact the NJ state tax authroities to see about a refund of the SUI and SDI taxes.

The SS and Medicare taxes withheld during the H-1B portion of your salary is correct and proper. You CANNOT successfully request a refund for those taxes.