I didn't work all year and my boyfriend did. Can he claim myself and/or my children on his return under other for relationship?

If your children lived all the year with your boyfriend, he can claim them as Qualifying Relative. Even then he will not get earned income credit for claiming the children. Your U.S. Tax Return: Requirements for claiming a dependent

Yes, he can claim YOU and YOUR children as dependents, but NO Child Tax Credit and NO Earned Income Credit if he is not the biological father.

I'd like to emphasize Mukata's statement that for your BF to claim you and the children you must have all lived with him for the entire year. And although you didn't ask about this: even if your BF claims you or the children as dependents he must still file as Single, not as Head of Household (unless he has other relatives living with him).

Good points, ebaines.