My boyfriend has been in me and my kids life for 4 years takeing care of me and my kids I go to school he supports us so can he clame them on his taxes

He can as long as no one else is eligible to claim them as dependents. If he is their sole or primary source of financial support then he should be able to claim them. How about their father? Does he pay child support? Is there any provision for claiming them as dependents in the support order? (Normally child support is not deductible to the payor nor claimable to the recipient.)

Your b/f can claim you and your kids as dependents as "Qualifying Relatives," if he meets the requirements. Since kids can not be his Qualifying Chidren, he will not get EIC.