Earned income credit has many qualifications. You haven't provided enough information to discuss the quaifications for most of them. For example he might make to much money. The children may not pass the relationship test. To be his qualifying child, a child must be his: Son, daughter, stepchild, eligible foster child, or a descendant of any of them (for example, your grandchild), or Brother, sister, half brother, half sister, stepbrother, stepsister, or a descendant of any of them (for example, your niece or nephew). You should review IRS Publication 596 (2012), Earned Income Credit (EIC).
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You are not married so it is unlikely your boyfriend cannot claim you as a dependent. If the children are not his, they are also not his dependents. As for earned income credit, you need to discuss this with a tax attorney or accountant. You have not furnished enough information.
Go to http://www.irs.gov/Individuals/EITC,-Earned-Income-Tax-Credit,-Questions-and-Answers to learn the rules about the Earned Income Tax Credit. To claim the EITC on your tax return, you must meet all of the following rules; (i) you, your spouse (if you file a joint return), and all others listed on Schedule EIC, must have a Social Security number that is valid for employment; (ii) you must have earned income from working for someone else or runnign or operating a farm or business; (iii) your filing status cannot be married filing separately; (iv) you must be a U.S. citizen or resident alien all year, or a NRA married to a U.S. citizen or resident alient and filing a joint return; (v) you cannot be a qualifying child of another person; (vi) you cannot file Form 2555 or Form 2555 ES (related to foreign earned income); (vi) you must meet the earned income, AGI and investment income limits (income limits change each year), see EITC Income limits for the tax year amounts; (viii) you must meet one of the following (a) have a qualifying child; (b) if you do not have a qualifying child, you must (1) be age 25, but under 65 at the end of the year (2) live in the US for more than half the year; and (3) not qualify as a dependent of another person.