@mattbrowne: Technically speaking, the amygdala is not responsible for memory. It appears to modulate memory encoding in the hippocampus, which is the part of your brain responsible for all conscious memories. Your statement that “two synapses are in between the olfactory bulb and the amygdala” is distinctly untrue.
The olfactory bulb (the part of your brain that gets information from your nose) sends thousands of projections directly to the centromedial nucleus of the amygdala, which projects directly to the basolateral nucleus of the amygdala. The basolateral nucleus has reciprocal projections to many areas of the cortex, but the relevant ones in this case are the olfactory cortex and the medial temporal lobe, which houses the hippocampus and surrounding cortex involved in declarative memory (the entorhinal cortex, the dentate gyrus, and the parahippocampal cortex).
None of these are considered “old” parts of your brain. The areas at the very base of your brain, responsible for crucial life functions (respiration, heart beat, etc) are the evolutionary oldest.
Anyway, the reason smell has such strong links to memory is because it assists the amygdala in modulating the hippocampus.