After about 5 minutes we started smelling a burning smell. We turned the crock pot off and assumed that the unit was defective. We later tried plugging it in to a normal outlet and it seemed to be working but the burnt smell lingered.

Later we plugged in our toaster to the same extension cord and it started to burn the unit.

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You probably have a bigger problem than the crock pot.  It sounds like you have a wiring problem with an unsafe wiring delivering too much current to the outlet.  The simple heating elements and circuitry of the toaster and the crockpot just pull the available current and convert it to heat.  They are being overwhelmed by the available currrent.  Left plugged in they are likely to start a fire.   The microwave is a bit more robust.  Probably doing power conversion with a transformer and able to handle a greater range of power inputs, and thus survive the funky powersource.

You could buy a small multimeter from your local hardware store and measure the voltage and current in the outlet, but a better bet is to call your landlord,  tell him you have an unsafe electrical problem and a fire hazard and have him send an electrician over to check out the electrical system.   I would strongly recommend not using that outlet or neighboring outlets (that includes any on the opposite side of that wall in another room) until it is checked out.