We made pickled reds with oj, lime, and salt. This is to mimic sour orange juice like you use for cochinita pibil.

To store in fridge should I keep them in the liquid or drain most of it? Is it like protein where it will break down into mush, or will it settle? How long should it keep since there isn't vinegar, a few days?

Who knows?! *uck around and let's find out! My guess is it's fine until the citrus starts to ferment. It's definitely not going to break down like meat will.

Maybe someone on here knows better but citrus juice oxidizes quickly, onions picked in lime juice might not last quite as long as those in a traditional pickling brine that's made from vinegar.