Your computer must be in sync to your ipad and that's why your are getting old emails. Delete them from your computer and that should fix it, or delete them from your ipad and they will be gone from your computer.
Same goes for smart phones.
Check your Spam (Yahoo) or Junk (Google) folder for junk mail or your trash. You can also do a search in email if you know the name of the file for which you are looking.
Be careful when entering contests or ordering on line. There is usually a box to check if you want to receive emails from the site....AND FROM THEIR PARTNERS. That's when the mailbox gets full.
Hope this helps.