Houses that cross rush with each other?

I don't really know what this means but the way rush works is: each houses talks to a PNM, the PNM ranks the house and the house gives the PNM a score. If she gets a high score she is likely to be invited back (if she likes that house). Low score, probably not. None of the houses discuss who they like or can see how a PNM is ranked by other houses.

Cross rush means which houses compete for the same PNMs?

It doesn't "work" a certain way at all; rush doesn't function that way, sororities don't function that way, tiers are made up based on people's opinions.

Each sorority has their own vibe and chapters with similar vibes tend to want the same pnm's, so you could consider that cross-rushing. It's nothing official though, it's just the way it happens to shake out. And it can change as pc's and memberships change every few years.

Some houses often do compete with each other for PNMs- Aphi/Kappa/Tri delt; DG/PHi Sig/AXO; and also Gphi/AXO; Kappa/Theta, SDT/AEphi.

And then, yes, there's typically a range of girls who pref a lot of different houses, of different competitiveness.

Keep in mind every year it's different and things to change over time, this is just an observation.