After a few days of searching, a clear explanation of these three concepts and how to study them is hard to find. I have a half-baked idea of these concepts but I feel I'm missing a lot. After seeing this post, it seems the word "allele" can mean different things depending on context making it harder for someone with a non-bio background to figure out. Here is what I've figured out so far:
What data is required to look at allele-specific binding and allele-specific expression?
ChIP-seq is used to look at protein binding sites, so allele-specific binding type of analyses are done with ChIP-seq data. RNA-seq is used to study gene expression, so allele-specific expression type of analyses are done with RNA-seq data.
How to study allele specific binding?
Suppose I have a reference genome and a chip-seq data set. After aligning the reads to the reference genome, I find all SNPs. In order to study allele-specific binding, this implies looking at only the heterozygous SNPs. How are allele-specific binding sites identified using a list of heterozygous SNPs?
Nathan Sheffield posted a good explanation of allelic imbalance here.