You need to create the directory
TEXMFHOME. That is, in your case, you need to create
~/Library/texmf and any subdirectories which you need below it.
For example, if you wanted to install
greatpackage.sty, you would create a directory
~/Library/texmf/tex/latex/greatpackage to contain it.
~/Library/texlive/2014/texmf-var is for auto-generated files. You can safely delete
~/Library/texlive/2014 and it will be recreated as and when necessary during compilation. You certainly should not install things into it! First, you might need to delete this directory in some cases. Second, TeX will look in
TEXMFHOME but not
.sty files etc.
It is normal for
TEXMFHOME not to exist until you create it. Not everyone needs this directory and, besides, a well-behaved installer ought not modify your home directory, as egreg mentioned in comments.
Indeed, upstream TeX Live recommend installing it as a non-root user and it is perfectly possible to install it as a non-root user other than yourself, in which case the installer could not modify your home directory, even if it wanted to do so. (For example, I manage my installation as
texlive:texlive precisely because doing so prevents the software from touching either system or home directories.)