Sounds like an old boyfriend of mine. He moved in with me, he said, because he wanted us to be together. I really wasn't in favor of it but I let him talk me into it. From the beginning I said we needed to split the bills 50/50 and he said okay, but he never gave me any money. It wasn't until he moved in with me that I realized how little he actually made at his job, and he also had kids (3) that he paid child support for--they took 60% of his paycheck out before he even got paid. I didn't begrudge him paying child support; I think it's great. But he wasn't honest with me about why he moved in with me--he was just looking for someone else to take care of him since he didn't have enough money to pay for his own place. Oh and he did the same thing your BF does; he always had money for cigarettes, beer, going out and having fun, but never for bills.
Don't do what I did: I put up with it until all my savings were gone, thinking surely things would change. And then I finally grew a brain (and some balls) and told him he needed to move out because I couldn't afford to take care of him any more. It was a big fight. He swore he'd get a better job, etc... I told him to get a better job and then we'd talk.
It's amazing how fast men can shape up when you give them an ultimatum; he found a better job within a week. He eventually moved back in and things were much better after that. I think he felt better about himself, too, for actually contributing to the household instead of being a mooch, especially when his oldest son came to live with us.
I guess the point I'm trying to make is sometimes you have to stand up for yourself. At least I had only me and no kids to worry about. I know you don't want to keep the kids away from their father. But I think if you put your foot down, you'll see what your BF is really made of. Either he'll shape up, or else you'll have gotten a monkey off your back, and you and your kids will be better of for it. You just have to be prepared to move forward no matter what the outcome is.
Get a job first, though! Even once you've signed up for WIC and welfare and whatever other assistance they may have where you live, you'll still need some income. Even if it's just fast food or waiting tables or cashiering somewhere, it's better than nothing. And the plus about those types of jobs is they're usually more willing to work with you on scheduling.
Good luck!