People that don't text back

[sodthediet]

I've recently became friends with my oh sister in law I find her very odd though.
In person she doesn't say much then she will text me soon as she leaves.

However when I text her back she doesn't text back but will text me again few days later with something else then won't text back again.

I don't get it really? Is this what people do now.

No I don't think it's that..... I think the clue is in what you wrote - you find her odd. This is one of the things she does which you find odd. I'd just roll with it as you're going to come across her as she's your partner's sister in law yes? People can be weird. It's not your problem and you don't have to solve it.