Oil Separators

Accumulator mainly in fixed orifice or capillary systems as there's no metering of liquid by demand (unlike TX valve systems that feed by demand), so the accumulator prevents liquid over flooding to the compressor. Also sometimes fitted on TXV low temp applications like freezers, to prevent floodback of liquid to the compressor.

Oil separators used when system design could cause poor oil return, eg compressor above the evap, or uneven oil return in the case of multiple compressors. Cheap insurance and costs less than heaps of pipework modifications

Receiver necessary for TX valve systems, all that refrigerant not being used because the TXV is closing due to low load, has to go somewhere.

oil separator required in the following applications
a) flooded chiller 
b) use of non-miscible refrigerant like ammonia application
c) all applications below evaporator temp (-20) deg C 
d) air-conditining systems where MOP valve is not used ; since non-MOP valves open fully during start up due to warm suction line & time required for the TEX valve to come to equilibrium .