[RPG] On weight limits of characters according to strength. Can a character carry his own weight

Nowhere in the books does it say that there are any special rules for a flying creature's carrying capacity so it's calculated the same as every other PC; Strength score multiplied by 15.

This is also unofficially backed by Jeremy Crawford, one of the lead designers for 5e, in a pair of tweets from May 2016:

Q: What are the rules for creatures carrying friendly PCs? e.g mage polymorphed into giant eagle carrying allies? (5e)

A: See "Lifting and Carrying" in the Player's Handbook (p. 176) for rules on carrying capacity.

Q: Are we to assume no adjustment for flying vs walking?

A: The carrying capacity rules make no distinction between walking and flying creatures.

Unless the backpack becomes a creature unto itself (via something like animate objects) it does not have a 'maximum' weight. Mostly because going down to that granular a level for random equipment is generally not worth the effort it would take. And, as you, yourself, pointed out, different materials can weigh different amounts, so there is no "standard" definition of how much a cubic foot of material weighs.

Carrying capacity is only affected by magical items, like muleback cords or a bag of holding (which only has an effect in that the things inside it weigh nothing in regards to your carrying capacity), or a masterwork backpack (which raises your effective str score by 1 when calculating carrying capacity). Containers such as barrels, waterskins, backpacks, etc... are more of a convenience for describing how your character is carrying all the random stuff adventurers carry.

As a gm, its far too much work and nowhere near fun enough for me to keep track of the size of everything to make sure it could fit in your various packs as long as it doesn't go over your carrying capacity. Also as a GM, I'd be insane or a giant pain to force my players to keep track of that as well. Saying that, though, its all about what I would deem as reasonable, you could probably throw 1000 coins, some pots and pans, food, and whatnot in a bag and I won't question it, but if you try and fit a 3.5 ft long sword in the bag and not have it be easy to steal, or trying to fit a small cursed item that weighs 1000 lbs in your bag without it ripping I'm gonna question you.

Essentially, its on a GM by GM basis.