So my party has gotten themselves into quite a pickle and one of our characters has gotten his mouth sewn shut by magical thread, which we can't cut. He is unable to eat and our GM has determined that he had roughly 4 days of being alright in that state without starving to death, we're now down to 1 1/2 days before he does starve and he has 2 levels of exhaustion which cannot be reduced from a long rest because he can't eat and drink. Is there any spell or creative solution to get him fed and allow us some more time to fix the whole situation?

He is a Tortle and the 'best' idea I've had is putting a feeding tube in his nose to keep him alive. He can't use a straw. He is a level 7 warlock.

Get creative

First the bad news. 5e does not seem to have a Ring of Sustenance like the earlier editions of D&D, and a Bead of Nourishment isn't going to help you if you can't get it in their mouth somehow. There are also no spells that can really help, there's no way to get a Goodberry inside the character's mouth. You might try to argue that a stomach is a container, but then Create Food and Water might instantly kill the character because it creates 45 gallons worth of food, which seems a bit excessive.

Instead, try to get rid of the magical thread so they can eat the normal way again.

The character had their mouth sewn shut by magical thread they can't cut, so cut around the magical thread and then figure out later how you're going to fix the poor Tortle's face later. Better to be a reptilian Joker than to starve to death.

Alternatively, see if you can nullify the magic of the thread. Perhaps there's a Dead Magic Zone that will do the trick, or perhaps the DM will be generous and agree that the wire itself is mundane and the magic keeping it from being cut is a spell cast on it, in which case Dispel Magic might work.

If that also doesn't work, there might be more drastic ways to keep the character from starving to death, such as using a spell or a monster to turn them to stone. A different, higher level solution would be to True Polymorph the character into a creature that doesn't need to eat, such as an undead or a construct.

A person with a knowelege of medicine might be able to create an incision and feed the character through that.

There are cows that have cannula fitted to their stomachs on a permanent basis that allow scientist to study their digestive systems and these live quite happily.

Your party could then either use magical foods like goodberries or beads of nourishment, or simply chew the food themselves before placing the chewed food directly into the party members stomach. Spells such as lesser restoration could be used as infection control to protect the site from infection.