Serious Applicants Only

Introduction. Mouths come in a wide variety of shapes and sizes and, physiologically speaking, no normal human has difficulty with those sounds. Impediments like dentures, braces, retainers, etc. can cause sudden changes in articulation, but these usually affect the tongue and its navigation of the oral cavity. Thus the basic answer to your broader question is: quite significant changes would be required.

Fangs. Specific to your question about fangs, there is a portion of the human population that have naturally pointy fangs. These do not affect articulation. There is also a portion of the population that wished they had pointy fangs and actually go to a cosmetic dentist to have pointy fangs installed. These are usually noticeably longer than natural pointy fangs --- perhaps 4 to 5 mm of point rather than 2 to 3 mm. These don't appear to affect articulation either.

Moderate changes. Speaking of significantly altering the skull structure, this is where we might begin to talk about changes to articulation. Two surgical procedures in particular significantly alter the oral landscape: the Lefort I proceedure and any kind of mandibular lengthening or shortening procedure. These are often done in patients with mid and lower facial deformities, severe overbite, etc. Some changes in speech are to be expected as the patient learns how to navigate a longer oral cavity. Therapy helps with this process.

Specific Phonemes. As for the specific sound changes you require, [stɹ] to [ʃtɹ] in English already exists as a variant in some dialects and there also seems to be some shifting in progress. (Pop back in after a couple centuries to see if it was just a fad or shall have became permanent!) Similarly, [ʊ] to [ʌ] exists. Precise placement of the tongue is really what determines which of the five basic S sounds you get. Pointy fangs don't really alter these sounds.

The most common situation that affects articulation is tonguetie. This is where the frenum (a little thin piece of tissue) holds the tongue tip down to the floor of the mouth. This results in difficulty producing dental & interdental sounds like T, D, TH, DH, S, Z, L.

Major Changes. You'd really have to do some kind of major changes to the human face to really affect articulation. Things like removing the tongue; removing the mandible; completely splitting the cheeks; severing the nerves supplying the oral and labial muscles, etc. There comes a point when the alteration will risk the health and perhaps life of the victim. Bottom line: the human mouth is versatile, agile, and able to articulate the sounds of language even with severe obstacles.

Brain-based

Don't change the mouth. Change the speech centers.

The changes are more than to anatomy. The digestive system must alter how it digests, the blood must carry food differently -- all this produces subtle brain changes as it adapts. If you like, it can be a result of malnourishment during the adaption, and be different from every vampire. Yours was so lucky as to affected only in the speech centers.

It would also be simple for her to overcome these problems over time, as a stroke victim can (sometimes) adapt.

Your character was born with an underbite. (Like 5-10% of the population are.)

This would mean that the upper canines poke-out inside the mouth, behind the lower teeth. This is right where the character is accustomed to having their tongue.

They need to be very careful when speaking so as to avoid double-skewering their tongue every time they say th, d, t etc..

They are able to make these sounds if they concentrate and articulate very carefully, but most times to get their point across they simply play it safe and keep the front of their tongue out the way.

Note:

It makes it trickier to bite necks, but that won't stop them when the blood-lust hits.

Filterfeeding like with baleen whales is out.

Filterfeeding like that is a mouth filling filter device- making it hard to utter sounds that way. Whales create their sounds via clicks from seperate oil fitted organs or by transferring the sound in other ways to water.

Tongues are the obvious criteria. Aras have tongues similar shapewise to humans and are similarly articulate, without the ability to shape the lips.

Meanwhile human company adapted animals like dogs or cats cannot recreate human sounds (although not for lack of trying, cats regularly mimic sounds - they connect to food or wished-for behaviour) but the tongue is not shaped to support it.

What caused the teeth to change?

As you've invoked the science-based tag, you need a biological cause for the change. Teeth are funny. Once they've grown, they're done. The processes that brought them into existence disappear. So you need something hanging around that results in this third change (first: baby teeth. Second: adult teeth). Look into the process of odontogenesis. Here's a simple version to get you going. Note that scientifically the adult teeth will not change. They must drop out just like your baby teeth did and be replaced by this third stage of tooth development.

Why is this important?

Because human gums aren't built to handle long canines. That means the shape of the soft palate and gums must change to handle their intended use. Wonderful! It isn't necessary for you to work out every detail of biology, simply mentioning that the gums and soft palate had to change allows you to declare that the vocal changes you want are a consequence.

But if you want a bit more... consider the following.

• Those canines must exist somewhere when the mouth is closed. They'll force the lower jaw back and push the cheeks out to cover them, changing the initial shape of the cheeks when speech begins.

• And it stinks to be a new vampire! Every stinking time you close your mouth, you cut into either the inside of your lower lip or the lower gums. Ouch! After a while your body builds callouses and scar tissue to stop the pain and bleeding... and those difficult-to-stretch patches of skin help rationalize your vocals.

• Finally, those long canines change how your mouth opens and closes. Now, this depends on just how long they are, but for the sake of argument, let's assume they're 3-5 times normal tooth length (yup, very long). Now imagine how you'd have to open and close your mouth to swing those puppies around!

Why do I like these reasons/rationalizations? Because they're story-based imaginative. Rather than talking about physiology (boring!) they're practical descriptions that your reader can relate to.