One of the only signifies that only one of the available one item or person is needed. The total number has always been one and just that is up for use.
"I need to mend one of the only pair of shoes I have."
One of the few signifies that one item or person out of an available series of choices or options even though little but decisions can still be made.
"You're one of the few people I actually want to talk to."
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