Basically what your boss, or whoever has the contract with that company needs to do is get the contract and find out at what point in it it says that equipment YOU own (I'm assuming that is the case) is not YOUR property and you have NO access to it. I've never heard of that in my life, typically when you do outside managed networks you provide them with login credentials (never the admin password, jsut an admin account) so they can get to what they need to. You, as a company always retain control in case you terminate the contract, etc. Sounds to me like they have weaseled their way in to having full control of the equipment, which is a little scary because you never know what they have running on it. For all you know they could be running a napster like service off of your equipment, and your internet line.
Before you go any further I'd find that information out, talk to your boss, or his boss, or whatever boss and dig up the contract. If it turns out the way I am thinking that you are not to be restricted, force it on them. Threaten to sue them for breach of contract, get control of the domain/Super Admin account back, change the password and then setup an account for them to use for the remainder of the time that has access to what they need. But that goes back to what exactly they "manage."
As for the servers:
Server 1.) If Exchange or whatever Email system you are using is removed from the server, that will free up alot of room. It sounds like it may be a small business server though which has a scaled down version of Exchange. Thats not all that bad. Typical larger exchange servers are clustered, with SAN module storage, etc. You'd have more then just 1 server for that. If its just a standard POP3 setup, those are typically easy enough to remove or setup and administrate.
If its keeping copies of profiles it sounds like you use roaming profiles at work. That typically allows a user to log into any computer on your network and have access to their data. That can be a pretty big space hog, but not terrible to mange.
One of them will have to be a print server, unless you use direct TCP/IP printing or some other method. When you add a printer to a computer, do you enter it by IP address, or do you do a "Find in the directory" and type in a name?
Server 2.) The server to house the accounting software, sounds like a stand alone server. Could be a database server as well depending on your application. one question to ask is does your software use SQL and does it have a SQL install on it, and would you be responsible for the backups and/or database work?
That could be a huge problem if you have little to no understanding of SQL and it is in fact using SQL, or SQL Express.
Alot of it sounds like information gathering. Goodluck with that.
Even a ghost needs to breathe.