It's not a general rule about th sounds. It depends on the actual word.
If it's the first two letters of them, you can reduce it, except in fairly formal speech.
Run 'em all together.
Similarly, you can reduce the first letter of her and him. But this doesn't apply to all th sounds:
The house 'at Jack built,
Jill is smarter 'n Jack,
both sound much more informal to me than dropping the th in them, although I expect both these reductions are common in informal speech. And
somewhere in 'air.
for "somewhere in there" just sounds wrong to me.
These are essentially weak forms of the words. Lots of structural words in English have weak forms; for example, there are weak forms of that, than, but, and just where the vowel changes to a schwa. These weak forms are perfectly acceptable in formal English. (And I believe these are often taught in ESL classes.)
The weak forms created by changing them, him, and her to /əm/, /əm/, and /ər/ are not quite as formal, but I would think they are acceptable in all but the most formal situations. The weak forms created by changing that and than to /ət/ and /ən/ are definitely informal, but still widely used in informal speech. And there is no weak form of there that is missing 'th'.