You'll probably never get a "virus" on an iPhone...malware on the other hand is a possibility, but up to this point, there have not been any. Apple patches security holes pretty quickly, and unless you have a jailbroken device, the chances of you running into malware is pretty much non-existant.
The "issue" you are describing is simply the email box self populating to the options you have in settings (last 50 emails, last 25 emails, etc)...so essentially, there's really not a problem, you're just getting your old emails on your phone, and when you delete them, it's sending the next batch of old emails. This is what commonly happens when a new email box is setup on an account with a lot of emails sitting in the inbox...the best solution, as mentioned above, is cleaning up your inbox and then setting up the email on the iPhone again.