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 1½ days before he starves and he has 2 levels of exhaustion (which cannot be reduced by taking 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.

The last version I played was version 2.5 (We wanted an upgrade but 3rd ... wasn't good for our group, so we created 2.5) and a little of 3rd.

If I remember right you can teleport stuff other than the caster teleporting himself. So plate of food = in his stomach. You can argue that even with a traditionally complicated spell with a marginal degree of error that can happen, the teleport is only going to be for a couple of feet or even measured in INCHES.

A rookie mage should be able to pull it off with ease as in the "crawling stages" of learning; he would have done this too may times to count as he worked his distance up through practice.

Our DM was awesome. He had a rule: if you can logically show how it is possible, even if its "against the rules" he would allow it. It created some very interesting games with interesting solutions to some interesting "puzzles".

One thing or phrase that was all over the place in the books (at least in the early ones) was "DM's Option!"

The more practical solution would be a simple feeding tube, or, a very good spot to introduce a "vampire' into the mix of characters as they do not need to really eat or drink(or some other form of "undead"), then his mouth can be sewn shut for eternity and depending on the party member, it might be a good addition to his character: the stitched mouth, not the addition of an undead. (Another fun thing DM did was tell us we rolling new characters.... then throw us the monsters manual to look through.)