You can certainly use W3TC and hook it in to Varnish to flush, but it’s complex and for the vast majority of people, something they don’t needs.
Tearstone: I can tell you’re still using bad behavior on the gaming site. I can see it in your wp-content folder right now, and when I run a check command, it shows as running and active on that site. If that isn’t the domain you want me to check on, let me know. You have a lot of plugins on a highly dynamic site, which runs for logged in users. That means you’re just not going to get the benefits of Varnish as much as other people, so … in YOUR case, W3TC might be a better call.
StephanieVega: Most of the time it IS a theme or plugin doing things in a funky way that doesn’t play nice with Varnish. On your site, you’ve got adrotate, which their developer says does not play well with Varnish. So that’s going to be a large part of your problem