meaning and usage of 'teh'

As tchrist and Matt Эллен tell you, this is 'eye dialect'. It doesn't represent any particular pronunciation: it's just JKR's way of signalling that you should 'hear' Hagrid speaking a non- or sub-standard variety of the language.

The inconsistency comes about because JKR's usual (and arbitrary) use of {ter} trips her up. JKR (and, presumably, Hagrid) speaks a non-rhotic dialect, so she naturally spells an unstressed to with an {r}, which to her (and generations of British writers) represents a contrast between 'proper' /tu/ and 'dialect' /tə/.

(Never mind the fact that that's how everybody actually pronounces to in most contexts).

But in most non-rhotic English dialects, when syllable-terminal /r/ occurs appears before a vowel it is pronounced, in effect as the head of the following syllable. JKR does not want to suggest the pronunciation /tərə/ for to a; so she changes her arbitrary {ter} to an equally arbitrary {teh}.

(Never mind the other fact that it is precisely in this context that most speakers, standard or non-, will actually pronounce to as /tu/. We're dealing with literary convention, not phonetic fact.)

HP 1 (Harry Potter and the Philosopher's/Sorcerer's Stone) was published in 1997, which I suppose was before the chat/text spelling {teh} for {the} became current. Or perhaps I am wrong in that supposition, and JKR was merely not at the time aware of the {teh} convention, either because she was too old (32) and too literarily educated (BA Exeter in French and Classics) to frequent circles where it was current or because she was too poor to have internet access.

This is nothing more than eye dialect, which per Wikipedia means simply:

Eye dialect is the use of nonstandard spelling for speech to draw attention to pronunciation. The term was originally coined by George P. Krapp to refer to the literary technique of using nonstandard spelling that implies a pronunciation of the given word that is actually standard, such as wimmin for women; the spelling indicates that the character’s speech overall is dialectal, foreign, or uneducated. This form of nonstandard spelling differs from others in that a difference in spelling does not indicate a difference in pronunciation of a word. That is, it is dialect to the eye rather than to the ear. It suggests that a character “would use a vulgar pronunciation if there were one” and “is at the level of ignorance where one misspells in this fashion, hence mispronounces as well.”

The term is less commonly also used to refer to pronunciation spellings, that is, spellings of words that indicate that they are pronounced in a nonstandard way. For example, an author might write dat as an attempt at accurate transcription of a nonstandard pronunciation of that.

Some notable authors who utilize eye dialect include Mark Twain, Joel Chandler Harris, William Faulkner, Robert Ruark, Charles Dickens, Alex Haley, Harriet Beecher Stowe, Terry Pratchett, and Russell Hoban.

However, most authors are likely to use eye dialect with restraint, sprinkling nonstandard misspelling here and there to serve as a cue to the reader about all of a character’s speech, rather than as an accurate phonetic representation.

While mostly used in dialogue, eye dialect may appear in the narrative depiction of altered spelling made by a character (such as in a letter or diary entry), generally used to more overtly depict characters who are poorly educated or semi-literate.

Eye dialect is often employed when authors wish to establish a sympathetic sense of superiority between themselves and the reader as contrasted with the nonstandard speech of the character. Such spellings serve mainly to “denigrate the speaker so represented by making him or her appear boorish, uneducated, rustic, gangsterish, and so on”. “The convention violated is one of the eyes, not of the ear”.

Note that beyond those you’ve yourself highlighted, o’ and yer and fer are all also eye-dialect examples in the supercited passage from Rowling’s first book.

It means to as well. i.e. "I wouldn't say no to a bit of your birthday cake."

It's just a different way of representing how Hagrid sounds.

Teh is a shortening of the pronunciation ter.

In spoken English, especially in British English, /ɑː/ can be shortened to /ɛ/ or /ə/ at the end of words.