Electric apartment sockets catching on fire
I'm not an electrical master, but I know this: outlets catching fire is NOT normal, ever. Furthermore, the apartment manager sounds like a real weasel. Outlets only cost a few dollars - in the face of a known fire risk, why waste time claiming nothing is wrong? Just replace the suspect part. You don't need an electrician, you need a new landlord.

That said, I understand sometimes people have reasons they can't move. At the very least, you should keep a fire extinguisher handy!

First of all, you do have a problem, so don't let anyone tell you everything is fine. Get an electrician of your own in there if you have to. This is a safety issue; life has no price tag.

Now, here are some questions I can think of that will help a professional figure out your problem:


Is it the same outlet that caught fire 4 times, or different
ones? 
Has the outlet that caught fire been replaced, only to have
the new one in the same location also catch fire? 
What is plugged into the outlets that catch fire? Is it always the same appliances
causing problems? 
How many appliances are plugged in to the problem outlets? 
Do any of the outlets seem loose?


If new outlets keep catching fire after you replace them, it could be a wiring issue, not an outlet issue.

If the outlets are seeing heavy current draw, from many appliances or a few big ones, it could be that the breaker on that circuit is too big for the associated wiring. An oversized breaker would allow more current through than the wires could handle. This could cause overheating.

If the outlets seem loose (and even if they don't) it could be that the wiring inside the  box, behind the outlet, is shorting out and causing sparks. I had GFI outlet that tripped all the time - I eventually discovered one of the terminals was arcing against the inside of the box.