Because Blades are Useful
I think you answered your own question about Gryffindor's sword. Goblin-made metal objects have certain magics about them that wizards can't replicate. (Remember in Harry Potter and the Deathly Hallows when Ron was arguing about Goblin/Wizard relations, said goblins can make armor and weapons wizards can't.) So it stands to reason that the sword would have properties superior to wand-use in certain circumstances.
So that leaves the other two, and I think the answer here is "they just happened to have knives on them." For Bellatrix it's a silver knife, which we know from Harry Potter and the Half-Blood Prince at least (When Harry borrows Hermione's 'silver knife' to crush ingredients for a potion) can be specifically required to make potions. What's more, it's obviously a common enough tool that year 6 Hogwarts students have them in their potion kits, rather than the school supplying them. (I assume Harry didn't have one because he wasn't prepared to take potions, whereas Hermione had bought all her NEWT Potions equipment.) So perhaps Bellatrix had the dagger on her because it's relatively small and handy to have with you for certain magic rather than in a drawer somewhere.
Also while not expressly stated in the Potterverse as far as I know, silver is known to be very effective against werewolves in western mythology. So Bellatrix may have had a silver knife on her person as insurance against Greyback. It's short because a small silver knife is more easily concealed and therefor won't arouse Greyback's suspicions. She uses it to cut Hermione's bonds for the same reason Mrs. Weasley tells Fred and George "not to whip your wands out for everything" in Harry Potter and the Order of the Phoenix. Namely that it's simpler on occasion to do tasks without magic. She already had a knife on her and it's simple and quick to cut rope with it, so she decided to use it rather than decide on a cutting spell, aim it, and cast it.
Bellatrix uses magic to cut the goblin a short time later. Why not use the knife? I think that's because of her feelings of "racial superiority". Why get dirty goblin blood on her hands if she can slice him from a distance? Then there's the simple act of using a magic wand on a goblin. Goblin's aren't allowed wands, so her using one on him is a show of her "racial superiority." Using a knife on the goblin might hurt him just as much, but doesn't send the same message.
Morfin's use of a knife I think boils down to his being unstable. He comes across as a poorly-educated sociopath. (Nailing a snake to your door when you know snakes are sentient and speak their language is a different and more serious thing than 'usual' animal torture in my opinion.) Maybe he likes the tactile feel of cutting into something as opposed to just using his wand? Maybe he isn't educated enough to know "cutting" spells, or talented enough to use them accurately if he does? Maybe snakes, though capable of rational thought to some extent, can't quite work out what a wand can do, but do understand knives and cutting. Thus waving a wand threateningly at a snake provokes no fear, but a knife does. "You be nice to Morfin or he'll nail you to the door" and the general vibe of that whole scene seems like Morfin's trying to scare/torture the snake more than anything. So a knife make sense. When Ogden arrives and the altercation begins, Morfin charges him with knife and wand because A: the knife is already in his free hand, so why not? and B: he might enjoy cutting Ogden with his own hands more than simply hexing him.