My boyfriend says he's evicting me and my minor children, while I have a broken neck, and cannot work or drive. How is this possible?

What state?
Disability and minors have nothing to do with right to evict.
He has to evict you for a reason, which can be failure to pay agreed rent or simply wanting the house for his personal use. He has to go through the formal steps required by your state.
You need to talk to the town social worker asap, or some relatives and friends.

He can have you formally evicted. He doesn't need a reason... he just needs to have you served and follow all applicible laws pertaining to the eviction process. Lacking a lease makes you a month to month tenant. He has to give you 30 days notice.

Sorry, but sometimes the law isn't nice or convenient. It is what it is. I would recommend contacting social services, friends etc... someone that can help arrainge for another place to go to.