"A couple" is exactly 2, excepting very specific downward exaggeration ("I'll only have a couple of beers.")
"Several" is always more than 2 but always a small number - say 3, 4, or 5.
"A few" is always more than 2 and probably more than several.
"Many" would normally exceed several, probably by quite a bit.
And of course "one" is always 1, excepting downwards exaggeration similar to a couple.
I do consider that "a couple" is imprecise and varies by context. Asking for a couple cloves of garlic while cooking could mean 2-4, especially if they are small. Asking for a couple bulbs of garlic on a shopping list could only mean 2!
For items, I think I'm also more like to shift into "half a dozen" or "dozen" than expect common ground on what "several" communicates. For days, I think I'd shift to "a week" or "N weeks" as soon as it spans a Monday-Friday work week, even if the start/end weeks are partial.
Context: in HoMM, a turn-based strategy game, you can see wandering "armies" in the world map, but cannot see the exact number of units in these armies unless you spent some points in scouting. What you do have is a verbal description of the army ("several trolls", "lots of faeries", etc.).
Those words always seemed the most fantastical to me
Maybe 'quite a few'?
I would say that "a couple" can also mean several. For example:
"Come back in a couple of days and we might have them in stock".
"Turn right where the old farmhouse used to be and they are a couple of k's down the road"
I'd allow that "a couple" could mean "2 that I'm certain about, but possibly 3 or maybe even 4".
I have to say I never thought there'd be that much disagreement among English speakers around the world on such basic terminology.
And what quantity is "quite a bit"?
Few and many also depend on context. "So few people voted last election" could mean 20,000,000 people, whereas "Many supreme court justices believe..." could refer to only four people.