If you make the "first year choice", you'll become a dual-status alien. Which means, you are non-resident until September 25th, and resident from that date on. That means you'll file two tax returns: 1040NR for the period when you're non-resident, and 1040 for the period you're resident, both for the same year. You'll pay the combined tax on both of them.
From Jan-Sep (no US income) do I have to file 1040NR and pay again
taxes in US for the Greek income?If yes How can adjust this tax?
For the period you're non-resident, you'll only have to report US-sourced income. If you have none - it will be an empty return.
For 25th Sept-31 Dec do I have to file 1040 with two W7 and request
ITIN for my wife and child correct?
What do I have to file for CA state
You're partial-year resident in CA (California, I'm guessing), and you'll file form 540NR. Similarly, until your residency starts (September 25th), you only report California-sourced income, after that - worldwide. Unfortunately, with California you don't have an option of filing as non-resident for the entire year, and you cannot offset foreign taxes. You'll be taxed twice.
how I will adjust the tax from foreign income?
On Federal tax return you can use form 1116 to calculate foreign tax credit for the period of your residency. You don't need to do any thing for the period when you're non-resident since the foreign income is not taxed.
You can also deduct foreign taxes on your Schedule A, instead of using foreign tax credit. In some cases, this may end up better for you, but you need to do the math. You need to remember that for both the deduction and the credit, you can only use the taxes you paid in Greece on earnings after September 25th.
Another alternative is to file as non-resident for the whole year, and only report the US-sourced income, and pay tax on that. You'll need to calculate all the options and choose the one that is the most beneficial for you.