how to make bash expand wildcards in variables?

You can write a function:

function expand { for arg in "$@"; do [[ -f $arg ]] && echo $arg; done }

then call it with what you want to expand:

expand "$MYDIR/"*.$SUFFIXES

You can also make it a script expand.sh if you like.

A deleted answer was on the right track. A slight modification to your attempt:

shopt -s extglob
MYDIR="./images"
OTHERDIR="./images/junk"  
SUFFIXES='@(pdf|eps|jpg|svg)'
mv "$MYDIR/"*.$SUFFIXES "$OTHERDIR/"

Brace expansion is done before variable expansion, but variable expansion is done before pathname expansion. So the braces are still braces when the variable is expanded in your original, but when the variable instead contains pathname elements, they have already been expanded when the pathname expansion gets done.

You'll need to eval that line in order for it to work, like so:

MYDIR="./images"
OTHERDIR="./images/junk"  
SUFFIXES='{pdf,eps,jpg,svg}'
eval "mv \"$MYDIR\"/*.$SUFFIXES \"$OTHERDIR/\""

Now, this has problems, in particular, if you don't trust $SUFFIXES, it might contain an injection attack, but for this simple case it should be alright.

If you are open to other solutions, you might want to experiment with find and xargs.