I can't help with finishing elastic as the knots I use always slide out and the beads go everywhere, so I will be interested to see what other people say, as I have some lovely beads that I would like to use with elastic.
I make most of my bracelets with memory wire and I have found that to get neat little loops the best pliers to use are long nose internal pliers - they dont have a serrated edge and therefore dont leave a ough finish, it also means you can add little beads on jump rings to finish off the ends.
They look like this:
I have found a lovely simple but effective bracelet to make is using 4 or 5 continuous loops of memory wire and threading seed beads and occasionally bigger beads - looks lovely and really cheap and simple to make - mine looked like this:
Hope that helps