I arrived in the US in April from the UK with my wife and 2 young children. I have an L1 visa and they L2's. My wife is not working. While I am here I am being paid from my company's Bermuda office.
What tax form should I file?
Does it cover whole year or from when I arrived?
Am I eligible for spouse/child credits?

Thanks
Stuart

You have completed substantial presence test in 2011 so you must report worldwide income on your US tax return.
Best option is to file joint return as residents and claim your children. On joint resident return you will both report worldwide income. With your tax return attach W7 (ITIN application) for your wife and children.
If you paid taxes in Bermuda and Bermuda has tax treaty with US, you can file form 1116 to claim foreign tax credit. You can also claim moving expenses.

Note that the tax treaty is NOT a requirement to file Form 1116 to claim the foreign tax credit.