They represent slightly different amounts/numbers in this order:
A couple = 2
A few = 3 or more, but not a lot (some people say 3 to 7)
Several = a moderate number of times
Many = a lot
In regular conversation, most people do not use strict definitions of these, and may use "a couple" and "a few" interchangeably, or "several" and "many" interchangeably.
It can depend on your intent. If you literally mean you heard something a certain number of times, you can choose the one that best represents the number you are referring to (if I heard something 4 or 5 times, I would say "a few").
I hope that is useful!