Below is a possible approach:

Step 1: Classify the mails in categories using the subject and/or message in the mail.

As you stated one category is of mails requesting position and the other is of mails of order. Machine Learning can be used to classify. You can use set of previous mails as training corpus. You might consider using NLTK(Natural Langauage Toolkit) for Python. Here is the link on text classification using NLTK.

Step 2: Once an email is identified as an order mail, process it to fetch the details(account name, size, time spread etc.) As you mentioned the challenge here is that there is no fixed format for these data. To solve this problem, you might consider preparing an exhaustive list of synonyms for each label(like for account the list could be like ['acct', 'a/c', 'account', 'acnt']). This should be done once, by going through a fixed volume of previous mails.

To make the solution more effective, you could consider implementing option for active learning (i.e., prompt the user if in a mail a lable is found which is not found in any list. E.g. in a mail, if "accnt" is used, it wont be resolved, hence user should be prompted to ask in which category it falls.)

Once a lable is identifies, you can use basic string operations, to parse the email in a fetch relevant data in structured format.

You can refer to this discussion for a better understanding.