How Are the Locks Supposed To Work?
 

I know the locks on my 83 300D aren't working correctly but how are they supposed to work? Is there a button somewhere for lock/unlock? Do they all automatically unlock when I unlock a front door with the key? Also, my back passenger door seems to be frozen. It wont open from the inside or out. It started out by being stuck with the door not closed properly. I tried giving it a little push to close it but nothing. I went for the door handle to open it and slam it shut and...nothing. Even though the door was unlocked it wouldn't open. The same happens from the inside. Does something need to be replaced or is this related to the locks not working correctly?

All doors unlock, including fuel inlet and trunk, when you unlock the driver's door.
All doors lock likewise when you lock the driver's door.

I doubt the rear door opening has something to do with the vacuum locks, but you can always locate the vacuum tube going to the door and try blowing/sucking into it to see if that has any effect. More than likely, there's a linkage disconnected in there.

You'll really need a vacuum tester- everyone here loves MityVacs- to troubleshoot the vacuum locks. Good luck!

Ok, so...no button for the locks? Just about every button in my car has been rubbed clean. I can't tell what a lot of things do. Thanks for the beta.

More than likely, someone has disconnected the vacuum line in the engine bay that feeds the door lock system. Once you get a mityvac, there is good information here to help you troubleshoot vacuum leaks. Its not that tricky, just takes some time.

As for the door that won't open, I think you can remove the rear door inner panel without having to open the door. Dieselgiant has a good pictorial for removing a door panel here.

As stated earlier, a linkage may have come loose, and you need to get to the inside of the door to check it out.

This is for a 300SD so there are differences (vac/pressure pump) but it might help.
http://www.peachparts.com/shopforum/showthread.php?t=150356

Here is the Vacuum Diagram "Stickey" thread.
http://www.peachparts.com/shopforum/showthread.php?t=105297&highlight=Vacuum+Diagrams

"Mighty Vac" is the name of a specific company. However, other companies make similar hand pump type Vacuum Testers. I would avoid the ones made of plastic as they could get damaged more easily than the metal ones.
This is a pic of the tester Harbor Freight sells for around $20. The better quality Vacuum Testers like the real Mighty Vac are around $40.

In this pic it is shown with the brake bleeding stuff. I bleed my Brakes with mine but I made a much larger jar.

Can the average person use their mouth to generate enough vacuum to open the door locks?

Don't get into the habit of opening the rear door to lock the car instead of using the key. I do that sometimes and one time the keys fell out of my jacket onto the seat and i locked myself out. :(
Had to make a sharpened hook out of a coat hanger, pry door open slightly with a long screwdriver and leather to protect the paint, and hook the button. Takes less than a minute if you have the theft tools. Too easy to break into these cars IMO.

Call Easy :P Elly @ 555-1212. :D

Probably, but it may require a lot of sucking. Three door actuators and the trunk actuator would require quite a bit of displacement.

I've tested them one at a time like that, can't imagine trying to do all at once.