When the air conditioner is turned on, the fan on the outside unit does not come on. What could these be?

check outside breaker see if it tripped. thermostat, low voltage wire going to outside unit or contactor on outside unit bad.

Turn it off NOW! Hope the unit didn't lockup.

The outside fan is used when ever the compresser needs to be cooled. So depending upon the outside temp as well as the temp of the refrigeration, it may not come on. When you say "our unit is ommiting a strange odor" are you refering to the outside condenser? or from the air handler? and what does it smell like? Please give us more to work with to be able to help you. Yes there are people looking and working on problems here at Fixya.com.

OUTSIDE FAN OR INSIDE FAN OR BOTH. IF BOTH CHECK THERMOSTAT WIRE HOOK UP. IF YOU INSTALLED NEW TSTAT CHECK FOR JUMPER ON RH-RC TERMINALS ON TSTAT BACK PLATE. IF INSIDE FAN COMES ON WITH FAN IN ON SETTING AT FAN ON AUTO LEVER THAN PROBLEM IS AT OUTSIDE UNIT. CHECK FUSES IN BOX ON OUTSIDE WALL. SHUT OFF BREAKER FIRST.

You will need to replace the outside fan,or condenser fan motor.
Shut unit down,before the compressor gets damaged.

Without the condensor fan the heat will not be blown to the outside air and the unit will not cool.

You may be low on freon too,have it checked.

Goodman air handlers (inside unit) fan have a delay timer that turn on the fan ,sometimes up to 3 minutes after the outside unit is on,this makes the a/c more efficiency.

clean outside fins and check freon level

replace start run capacitor of motor fan

Even when the power is off at the unit outside the thermostat will supply power to the contactor of the outside unit. This may give a hum or buzz as you stated. If when the power is on to the outside unit the fan tries to start but only hums the motor may be bad. Does the compressor start and run?

if its a a window unit suspect a faulty fan capacitor or bad fan motor same with outside, if it ain't moving or turning on the fan is faulty or the capacitor is faulty