For that volume of emails it doesn't look like someone is bulk mailing from your account. There is a popular PHP shell that phones home via email every time the shell is loaded which could account for that volume of emails. If you have shell access then try this from the root directory of your blog:
Pretty fucked up that your host is not solving the problem though. That's shitty support. I was with Amerinoc back when it was Phatservers and I thought it was shit. I dunno if they still do, but they used this backward Directadmin interface and everything about it just sucked.