I have a boyfriend who has lived with me for 3yrs he doesn't work and I am the sole provider. He has 2 children that live with us he has custody and I take care of them. Can I claim his kids on my taxes? And do I qualify for a earned income tax credit?

No. If you were married to him you can take the tax deduction and also the earned income tax credit as the children would be your stepchildren. Boyfriends don't count - husbands do. Sorry.

You can claim your b/f as dependent (as Qualifying Relative) only if
1. He lived with you all the year,
2. he did not earn more than $3,650 in 2009, and
3. Your relationship does not violate local law. Your U.S. Tax Return: Requirements for claiming a dependent

If you can claim you b/f and his kids live with you, you can also claim the kids and get exemptions, but you will not get EIC as the kids are not your qualifying children.

Agreed; now, if you get hitched in the next three days and are legally married by midnight on 31 Dec 09, then (and only then) could you qualify for the Earned Income Credit.