Please note that each Senate office will handle mail slightly different, however this post is general enough that it should apply most everywhere.
I will only be talking about mail from constituents, meaning people who are writing their duly elected representatives, and not someone else's. (See journal post of do's and don't of contacting your senator.)
Also please know that there is a delay in your mail reaching your Senator (it's about 3 days right now).
I'm going to split the mail into three sections, snail mail (regular mail), electronic mail, and batch mail. I'll start with batch mail first, since it includes mail that alone would fall into snail or electronic.
This is any type of mail that is a form letter or a petition, postcard, or in some cases organized mass mailing campaign. Each Senate office receives tens of thousands of these types of letters each year - both via email, fax and via the post office. Sometimes the people that submit them will submit the same letter multiple times (especially if it is electronic mail since it is so easy to resend it). It is treated the same in the beginning like all other mail. It is sorted and logged in. However, it receives a form response. The response may be updated several times a year if the situation changes, although this is not likely. The Senator will never view this type of mail, and it may not even make it up the chain to a Legislative Assistant. It carries an extremely low impact.
There are reasons why this type of mail has almost no impact. The main one being people that sign a petition or participate in a form mailing often meet one of several criteria. One, they are unaware their name is being used. (This is true - sometimes political groups will pull names from organizations and even phone books, without consent from every member of the organization or people in the phone book.) Two, they often are not fully informed on all sides of the issue. They only know what the people that had them sign the petition told them and do not see the other side. Lastly, these type of people usually are one issue people and will vote based on that one issue already, so there is little we can do to influence them or help them get involved in the political process. A small Senate office will average upwards of 50,000 batch constituent communications in a year.
This is any type of mail that comes via regular post from packages to written or typed letters that is not a batch communication. This type of communication is logged in and sorted and then assigned to a legislative correspondent. Usually this type of mail falls into one of two categories - rational or irrational. Rational is where the person has researched their question and is asking for a legitimate response. They will get a personalized response and their letter will travel up the chain of command. The Senator may read it in fact. It will take longer to answer because some thought and research will go into it and usually a Legislative Assistant will be consulted for advice. They are sadly, the minority of letters that we receive. Irrational mail is those that are emotional appeals, ones that complain of aliens (the new one this week is microwave beams mounted in car headlights) or ones that say "Do xxxxx" or "Enact this now" without any basis for why or reasoning. They will not include facts, suggestions, how legislation is impacting them personally and what their friends think. If they do, usually their facts are inaccurate (like the large number we're getting which claim the Moon landing was faked). These type of irrational letters rank even lower than batch mail. They may not be answered by some offices or if they are, they are assigned to an intern to answer. We do check them for threats though, since a fair amount of crazy people which have attacked people on the Hill have written in first.
This section includes faxes, emails and for purposes phone calls. Phone calls are logged in just like mail and receive a response, although it depends a lot on the person that records the call and the message the call conveyed. If the caller is polite and the person recording the message is competent and not rushed, they are an effective way of conveying an opinion. E-mails are the other large amount of mail that a senate office receives. Each office probably receives upwards of 500,000 pieces of email a year (after spam). Thankfully, most of the email is not from constituents, it is from organized mail campaigns or people that simply live out of state that are emailing every Senator. This is sorted first, and then logged in. Due to the large volume (still a lot when all the out of state mail is excluded) it is harder to pick out the gems of letters from the hundreds of batch letters, since organizations which send in batch emails often will modify their email templates (or have the sender type a couple of sentences at the bottom) to make it seem more personal (or we would just detect them and route them differently. They are then answered like snail mail. Faxes are the last major type of electronic mail that we receive. Faxes are often spam. However, since many organizations with important publications / needs for earmarks also send their information in by fax or people wishing to make an appointment with the Senator will submit requests by fax, it is harder to filter for spam in the beginning. This means that a large amount of spam gets through. This makes sorting faxes tough for whoever does it in the office. They are logged in or routed to appropriate staff and then answered.
How much mail does an office receive in a year?
I have a friend that works in another office - one of the smallest since his state has a small population (one of the smallest). They recently logged in 110,000 pieces of mail for the year.