I'm 18, married, and live in Kentucky. She's 14 and lives with our little brother, my mother and her boyfriend (the father of my brother and sister), my uncle and his girlfriend, and our cousin/ her kids in Ohio. They've lived there for about 10 months.
To make a long story very short:
-My parents are addicted to illegal substances.
-The other members of the household also traffic drugs in and out of the home.
-We've been to foster homes in Kentucky twice over my parent's addiction.

I haven't lived with my mother/her family for long - I moved in with my mother when I was 11 and moved right back out when I was 14. During the three years I was there, we were homeless more than twice, our utilities were shut off numerous times, we had two instances of being in foster homes, and the list goes on. She allowed me to move out at 14 years old and I went to live with my friend and later, my boyfriend and his family. She has tremendous personality defects when I presume to be caused my addiction. If needed, there are plenty of people who would gladly be a character witness regarding this information.

In addition to this, my 'step dad' (although they're not legally married, they've been together for 14 years) is currently dodging warrants he has here in Kentucky for theft. I'm not 100% certain of the details.

My sister wants to live with me and my brother doesn't, but I'm afraid I wouldn't be able to get custody - and instead they both would have to go back to a foster home. I have a two bedroom apartment, but I'm married and we have a housemate. She's been living with me for two months now - but my parents won't grant me custody and are in the process of demanding she be returned next weekend to live with them. At this time, I'm not employed - but we do have a household income. I have her enrolled in school here (I did so by saying my mother lives with me but was out of state at the time) and we've been comfortably supporting her since she's been here.

What can I do to get custody of her?

Trying to get custody without mom's OK is probably doomed to the result of you not getting your sister and she and her brother going into foster care. You are articulate and could try, but the odds are very much against you. You are 18, your finances are unclear, you have another roommate bringing in income so either don't have a bedroom for your sister or lose some income if you do, and you have lied to get her into school. It just isn't going to work, I'm afraid.

I agree, you are not on solid footing. You have lied, her legal parents oppose your getting custody. You need to return her to her legal parents or, at least to family services, then try to get guardianship.