Well, a *.sde file is a SDE connection file. It basically saves all the connection properties for connecting to a SDE geodatabase. It saves things like database, version, username, password (optionally), etc... This is commonly used to connect to SDE geodatabases, especially in enterprise level implementations of ArcGIS Server technology. You can read those files easily by navigating to them with ArcGIS Desktop software and then right clicking on them and checking out their connection properties and geodatabase connection properties. Multiple *.sde files are often present due to either them being used to connect to one database in a variety of ways (various versions such as DEFAULT, QA/QC version, Editor1, Editor2, Project1, etc...) or multiple files could be present because they could be connections to a variety of geodatabases on your server(s) (main database on production server, main database on testing server, internal project database on production server, etc...), or some combination there-of. Also, as far as why they would be on that pc, well, if that machine was ever used to run ArcGIS Desktop, they could have been created by the user and never been deleted, or, and potentially the more likely case from your description, if the PC was more or less being used as shared network storage, those files could have been put there to allow anyone on your network who has ArcGIS Desktop to navigate to those files and be able to connect to the appropriate versions of the appropriate geodatabses without knowing the specific connection properties for each database.
Example, there could be something like historic_version_of_main_production_db_before_projectXYC_completion.sde referencing a historic version connection that someone saved out to the pc so that anyone in your organization connecting to the PC could pull in the data of exactly how everything looked in the database before a certain project was completed, without them having to look up the details and figure out how to set up such a connection themselves. That way anyone could pull in that data and do their own comparison maps/analysis as needed. That's just one example, but hopefully it helps give you an idea.
The following link may help give you some ideas about the files. It is a doc about creating SDE connection files, but, the info is still relevant to understanding what they are also. http://help.arcgis.com/en/arcgisdesktop/10.0/help/index.html#//0017000000pt000000